Solve for all values of x by factoring. x^(2)-12 x+35=0 Answer: x=

Identify a, b, c: Identify a, b, and c in the quadratic equation x^2 - 12x + 35 = 0. Compare x^2 - 12x + 35 with ax^2 + bx + c. a = 1 b = -12 c = 35Find Product and Sum: Find two numbers whose product is a*c (which is 35) and whose sum is b (which is -12). We need to find two numbers that multiply to 35 and add up to -12. The numbers -5 and -7 satisfy these conditions because: -5 * -7 = 35 -5 + -7 = -12Write Factored Form: Write the quadratic equation in its factored form using the numbers found in Step 2. The factored form of the equation is: (x - 5)(x - 7) = 0Solve for x: Solve for x by setting each factor equal to zero. First factor: x - 5 = 0 x = 5 Second factor: x - 7 = 0 x = 7

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve for all values of

x

by factoring.

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x^{2}-12 x+35=0

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Answer:

x=

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic equation $x^2 - 12x + 35 = 0$ . Compare $x^2 - 12x + 35$ with $ax^2 + bx + c$ . $a = 1$ $b$ $0$ $b$ $1$
Find Product and Sum: Find two numbers whose product is $a*c$ (which is $35$ ) and whose sum is $b$ (which is $-12$ ). $\newline$ We need to find two numbers that multiply to $35$ and add up to $-12$ . $\newline$ The numbers $-5$ and $-7$ satisfy these conditions because: $\newline$ $-5 \times -7 = 35$ $\newline$ $-5 + -7 = -12$
Write Factored Form: Write the quadratic equation in its factored form using the numbers found in Step $2$ . $\newline$ The factored form of the equation is: $\newline$ $(x - 5)(x - 7) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ First factor: $\newline$ $x - 5 = 0$ $\newline$ $x = 5$ $\newline$ Second factor: $\newline$ $x - 7 = 0$ $\newline$ $x = 7$