Solve the quadratic by factoring. x^(2)-8x=8x-63 Answer: x=

Write Equation: Write down the given quadratic equation. x^2 - 8x = 8x - 63Rearrange Terms: Move all terms to one side of the equation to set it to zero. x^2 - 8x - 8x + 63 = 0 Combine like terms. x^2 - 16x + 63 = 0Factor Equation: Factor the quadratic equation. We need to find two numbers that multiply to 63 and add up to -16. The numbers -7 and -9 satisfy these conditions because: -7 * -9 = 63 -7 + -9 = -16 So, we can write the factored form as: (x - 7)(x - 9) = 0Set Factors to Zero: Solve for x by setting each factor equal to zero. x - 7 = 0 or x - 9 = 0 Solve each equation for x. x = 7 or x = 9

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve the quadratic by factoring.

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x^{2}-8 x=8 x-63

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Answer:

x=

Write Equation: Write down the given quadratic equation. $\newline$ $x^2 - 8x = 8x - 63$
Rearrange Terms: Move all terms to one side of the equation to set it to zero. $\newline$ $x^2 - 8x - 8x + 63 = 0$ $\newline$ Combine like terms. $\newline$ $x^2 - 16x + 63 = 0$
Factor Equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $63$ and add up to $-16$ . $\newline$ The numbers $-7$ and $-9$ satisfy these conditions because: $\newline$ $-7 \times -9 = 63$ $\newline$ $-7 + -9 = -16$ $\newline$ So, we can write the factored form as: $\newline$ $(x - 7)(x - 9) = 0$
Set Factors to Zero: Solve for $x$ by setting each factor equal to zero. $x - 7 = 0$ or $x - 9 = 0$ Solve each equation for $x$ . $x = 7$ or $x = 9$