College Algebra Extra Credit

1. Solve for the quadratic equation for x. 4x² + 16x = 48

The correct answer is x = 2, -6. This is because when we solve the quadratic equation 4x^2 + 16x = 48, we can rearrange the equation to 4x^2 + 16x - 48 = 0. By factoring or using the quadratic formula, we find that x = 2 and x = -6 are the solutions to the equation.

Explanation

The correct answer is x = 2, -6. This is because when we solve the quadratic equation 4x^2 + 16x = 48, we can rearrange the equation to 4x^2 + 16x - 48 = 0. By factoring or using the quadratic formula, we find that x = 2 and x = -6 are the solutions to the equation.

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2. What type of equation is this? Explain using terms we discussed in class. If you use an explanation we did not discuss in class, I will assume you used the internet.

3(2x + 1) - x + 4 = 2

This equation is a linear equation because it is in the form of ax + b = c, where x is the variable and a, b, and c are constants. In this equation, 3(2x + 1) represents the coefficient of x, -x represents the coefficient of x, and 4 represents the constant term. The equation can be simplified and solved to find the value of x, which makes it a linear equation.

Explanation

This equation is a linear equation because it is in the form of ax + b = c, where x is the variable and a, b, and c are constants. In this equation, 3(2x + 1) represents the coefficient of x, -x represents the coefficient of x, and 4 represents the constant term. The equation can be simplified and solved to find the value of x, which makes it a linear equation.

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3. (Disregard the number 13)Show your work for the problem below using all steps we discussed in class. On a separate sheet of paper, explain what type of equation it is and why you have two answers.

A. (see above)

B. (see above)

C. (see above)

D. (see above)

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Explanation

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4. What is the greatest common factor (GCF) in the problem below? On your scratch paper, explain why you picked your answer. 3x² - 18x - 42 = 6

The greatest common factor (GCF) is the largest number that can evenly divide all the terms in the given equation. In this equation, the terms are 3x^2, -18x, -42, and 6. When we factor out 3 from each term, we get 3(x^2 - 6x - 14) = 6. Since 3 is a common factor that can evenly divide all the terms, it is the greatest common factor (GCF) in this problem.

Explanation

The greatest common factor (GCF) is the largest number that can evenly divide all the terms in the given equation. In this equation, the terms are 3x^2, -18x, -42, and 6. When we factor out 3 from each term, we get 3(x^2 - 6x - 14) = 6. Since 3 is a common factor that can evenly divide all the terms, it is the greatest common factor (GCF) in this problem.

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6. Solve for the quadratic equation for x. 2x² + 84 = 26x

The quadratic equation given is 2x^2 + 84 = 26x. To solve for x, we need to rearrange the equation to bring all terms to one side and set it equal to zero. By subtracting 26x from both sides and rearranging the terms, we get 2x^2 - 26x + 84 = 0. This is a quadratic equation in standard form. To solve it, we can either factor it or use the quadratic formula. After factoring or using the quadratic formula, we find that the solutions for x are 6 and 7.

Explanation

The quadratic equation given is 2x^2 + 84 = 26x. To solve for x, we need to rearrange the equation to bring all terms to one side and set it equal to zero. By subtracting 26x from both sides and rearranging the terms, we get 2x^2 - 26x + 84 = 0. This is a quadratic equation in standard form. To solve it, we can either factor it or use the quadratic formula. After factoring or using the quadratic formula, we find that the solutions for x are 6 and 7.

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7. What type of equation is this? Explain using terms we discussed in class. If you use an explanation we did not discuss in class, I will assume you used the internet. On your scratch paper, solve the equation and show all steps. x² - 16x - 20 = -3

X = -17, -1

X = 1, -17

X = 17, -1

X = 1, 17

This is a quadratic equation because it has a degree of 2. In class, we learned that quadratic equations can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants. In this equation, the coefficients are 1, -16, and -20, and the constant term is -3. To solve the equation, we can use the quadratic formula or factor the equation if possible. After solving, we find that the solutions are x = 17 and x = -1.

Explanation

This is a quadratic equation because it has a degree of 2. In class, we learned that quadratic equations can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants. In this equation, the coefficients are 1, -16, and -20, and the constant term is -3. To solve the equation, we can use the quadratic formula or factor the equation if possible. After solving, we find that the solutions are x = 17 and x = -1.

8. Solve for x using the square root method. Show your work on scratch paper and explain your answers. 5x² + 9 = 14

Not able to solve

X = -1, -1

X = 1

No solution

X = 1, -1

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Explanation

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