Solve the quadratic by factoring. x^(2)-10 x=2x-35 Answer: x=

Write Equation: Write down the original equation. x^2 - 10x = 2x - 35Rearrange Terms: Move all terms to one side of the equation to set the equation to zero. x^2 - 10x - 2x + 35 = 0 Combine like terms. x^2 - 12x + 35 = 0Combine Like Terms: Factor the quadratic equation. We need to find two numbers that multiply to 35 and add up to -12. The numbers -5 and -7 fit this requirement because: (-5) * (-7) = 35 (-5) + (-7) = -12 So the factored form is: (x - 5)(x - 7) = 0Factor Quadratic: Solve for x by setting each factor equal to zero. x - 5 = 0 or x - 7 = 0 Solving each equation gives us: x = 5 or x = 7

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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}-10 x=2 x-35

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Answer:

x=

Write Equation: Write down the original equation. $\newline$ $x^2 - 10x = 2x - 35$
Rearrange Terms: Move all terms to one side of the equation to set the equation to zero. $\newline$ $x^2 - 10x - 2x + 35 = 0$ $\newline$ Combine like terms. $\newline$ $x^2 - 12x + 35 = 0$
Combine Like Terms: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $35$ and add up to $-12$ . $\newline$ The numbers $-5$ and $-7$ fit this requirement because: $\newline$ $(-5) \times (-7) = 35$ $\newline$ $(-5) + (-7) = -12$ $\newline$ So the factored form is: $\newline$ $(x - 5)(x - 7) = 0$
Factor Quadratic: Solve for $x$ by setting each factor equal to zero. $x - 5 = 0$ or $x - 7 = 0$ Solving each equation gives us: $x = 5$ or $x = 7$