Solve the quadratic by factoring. x^(2)+13 x-22=6x+8 Answer: x=

Write Standard Form: Write the quadratic equation in standard form by moving all terms to one side of the equation. x^2 + 13x - 22 = 6x + 8 Subtract 6x and 8 from both sides to get: x^2 + 13x - 6x - 22 - 8 = 0 Combine like terms: x^2 + 7x - 30 = 0Factor Quadratic Equation: Factor the quadratic equation. We need to find two numbers that multiply to -30 and add up to 7. The numbers 10 and -3 satisfy these conditions because: 10 * -3 = -30 10 + (-3) = 7 So we can write the factored form as: (x + 10)(x - 3) = 0Solve for x: Solve for x by setting each factor equal to zero. x + 10 = 0 or x - 3 = 0 Solve each equation for x: x = -10 or x = 3

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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}+13 x-22=6 x+8

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Answer:

x=

Write Standard Form: Write the quadratic equation in standard form by moving all terms to one side of the equation. $\newline$ $x^2 + 13x - 22 = 6x + 8$ $\newline$ Subtract $6x$ and $8$ from both sides to get: $\newline$ $x^2 + 13x - 6x - 22 - 8 = 0$ $\newline$ Combine like terms: $\newline$ $x^2 + 7x - 30 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $-30$ and add up to $7$ . $\newline$ The numbers $10$ and $-3$ satisfy these conditions because: $\newline$ $10 \times -3 = -30$ $\newline$ $10 + (-3) = 7$ $\newline$ So we can write the factored form as: $\newline$ $(x + 10)(x - 3) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x + 10 = 0$ or $x - 3 = 0$ $\newline$ Solve each equation for x: $\newline$ $x = -10$ or $x = 3$