Solve the quadratic by factoring. x^(2)-33=6x-6 Answer: x=

Write Standard Form: Write the quadratic equation in standard form. To solve the quadratic equation by factoring, we need to bring all terms to one side of the equation to set it equal to zero. x^2 - 33 = 6x - 6 Subtract 6x and add 6 to both sides to get: x^2 - 6x - 33 + 6 = 0 Simplify the equation: x^2 - 6x - 27 = 0Factor Quadratic Equation: Factor the quadratic equation. We need to find two numbers that multiply to -27 and add up to -6. The numbers -9 and 3 satisfy these conditions because: -9 * 3 = -27 -9 + 3 = -6 So we can write the factored form as: (x - 9)(x + 3) = 0Solve for x: Solve for x. Set each factor equal to zero and solve for x: x - 9 = 0 or x + 3 = 0 x = 9 or x = -3

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Solve the quadratic by factoring.

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x^{2}-33=6 x-6

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Answer:

x=

Write Standard Form: Write the quadratic equation in standard form. $\newline$ To solve the quadratic equation by factoring, we need to bring all terms to one side of the equation to set it equal to zero. $\newline$ $x^2 - 33 = 6x - 6$ $\newline$ Subtract $6x$ and add $6$ to both sides to get: $\newline$ $x^2 - 6x - 33 + 6 = 0$ $\newline$ Simplify the equation: $\newline$ $x^2 - 6x - 27 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $-27$ and add up to $-6$ . $\newline$ The numbers $-9$ and $3$ satisfy these conditions because: $\newline$ $-9 \times 3 = -27$ $\newline$ $-9 + 3 = -6$ $\newline$ So we can write the factored form as: $\newline$ $(x - 9)(x + 3) = 0$
Solve for x: Solve for x. $\newline$ Set each factor equal to zero and solve for x: $\newline$ $x - 9 = 0$ or $x + 3 = 0$ $\newline$ $x = 9$ or $x = -3$