Solve for all values of x by factoring. x^(2)-9x+3=-5 Answer: x=

Rewrite Equation: Rewrite the equation to set it equal to zero. We start by adding 5 to both sides of the equation to set the right side to zero. x^2 - 9x + 3 + 5 = 0 x^2 - 9x + 8 = 0Factor Quadratic: Factor the quadratic equation. We need to find two numbers that multiply to 8 (the constant term) and add up to -9 (the coefficient of the x term). The numbers that satisfy these conditions are -1 and -8 because: -1 * -8 = 8 -1 + -8 = -9 So we can factor the quadratic as: (x - 1)(x - 8) = 0Solve for x: Solve for x by setting each factor equal to zero. If (x - 1)(x - 8) = 0, then either (x - 1) = 0 or (x - 8) = 0. Solving each equation for x gives us: x - 1 = 0 => x = 1 x - 8 = 0 => x = 8

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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}-9 x+3=-5

\newline

Answer:

x=

Rewrite Equation: Rewrite the equation to set it equal to zero. $\newline$ We start by adding $5$ to both sides of the equation to set the right side to zero. $\newline$ $x^2 - 9x + 3 + 5 = 0$ $\newline$ $x^2 - 9x + 8 = 0$
Factor Quadratic: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $8$ (the constant term) and add up to $-9$ (the coefficient of the $x$ term). $\newline$ The numbers that satisfy these conditions are $-1$ and $-8$ because: $\newline$ $-1 \times -8 = 8$ $\newline$ $-1 + (-8) = -9$ $\newline$ So we can factor the quadratic as: $\newline$ $(x - 1)(x - 8) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ If $(x - 1)(x - 8) = 0$ , then either $(x - 1) = 0$ or $(x - 8) = 0$ . $\newline$ Solving each equation for x gives us: $\newline$ $x - 1 = 0$ => $x = 1$ $\newline$ $x - 8 = 0$ => $x = 8$