Solve the quadratic by factoring. x^(2)-36=x-6 Answer: x=

Rewrite Equation: Rewrite the equation to set it equal to zero. We need to bring all terms to one side of the equation to set it equal to zero. x^2 - 36 - x + 6 = 0 Combine like terms. x^2 - x - 30 = 0Combine Like Terms: Factor the quadratic equation. We need to find two numbers that multiply to -30 and add up to -1 (the coefficient of x). The numbers -6 and 5 satisfy these conditions because -6 * 5 = -30 and -6 + 5 = -1. So we can factor the quadratic as: (x - 6)(x + 5) = 0Factor Quadratic Equation: Solve for x using the zero product property. If (x - 6)(x + 5) = 0, then either x - 6 = 0 or x + 5 = 0. Solving x - 6 = 0 gives us x = 6. Solving x + 5 = 0 gives us x = -5.

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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}-36=x-6

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Answer:

x=

Rewrite Equation: Rewrite the equation to set it equal to zero. $\newline$ We need to bring all terms to one side of the equation to set it equal to zero. $\newline$ $x^2 - 36 - x + 6 = 0$ $\newline$ Combine like terms. $\newline$ $x^2 - x - 30 = 0$
Combine Like Terms: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $-30$ and add up to $-1$ (the coefficient of $x$ ). $\newline$ The numbers $-6$ and $5$ satisfy these conditions because $-6 \times 5 = -30$ and $-6 + 5 = -1$ . $\newline$ So we can factor the quadratic as: $\newline$ $(x - 6)(x + 5) = 0$
Factor Quadratic Equation: Solve for $x$ using the zero product property. $\newline$ If $(x - 6)(x + 5) = 0$ , then either $x - 6 = 0$ or $x + 5 = 0$ . $\newline$ Solving $x - 6 = 0$ gives us $x = 6$ . $\newline$ Solving $x + 5 = 0$ gives us $x = -5$ .