Solve for all values of x by factoring. x^(2)+3x-42=4x 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 + 3x - 42 - 4x = 0 Combine like terms. x^2 - x - 42 = 0Factor Quadratic: Factor the quadratic equation. We need to find two numbers that multiply to -42 and add up to -1 (the coefficient of x). The numbers -7 and 6 work because -7 * 6 = -42 and -7 + 6 = -1. So we can factor the equation as: (x - 7)(x + 6) = 0Solve for x: Solve for x using the zero product property. If the product of two factors is zero, then at least one of the factors must be zero. So we set each factor equal to zero and solve for x: x - 7 = 0 or x + 6 = 0 x = 7 or x = -6

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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.

\newline

x^{2}+3 x-42=4 x

\newline

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. $\newline$ $x^2 + 3x - 42 - 4x = 0$ $\newline$ Combine like terms. $\newline$ $x^2 - x - 42 = 0$
Factor Quadratic: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $-42$ and add up to $-1$ (the coefficient of $x$ ). $\newline$ The numbers $-7$ and $6$ work because $-7 \times 6 = -42$ and $-7 + 6 = -1$ . $\newline$ So we can factor the equation as: $\newline$ $(x - 7)(x + 6) = 0$
Solve for x: Solve for x using the zero product property. $\newline$ If the product of two factors is zero, then at least one of the factors must be zero. $\newline$ So we set each factor equal to zero and solve for x: $\newline$ $x - 7 = 0$ or $x + 6 = 0$ $\newline$ $x = 7$ or $x = -6$