Solve the quadratic by factoring. x^(2)+22=-9x+4 Answer: x=

Write Standard Form Equation: Write the equation in standard form. We need to bring all terms to one side of the equation to have it in the form ax^2 + bx + c = 0. x^2 + 22 = -9x + 4 Add 9x to both sides and subtract 4 from both sides to get: x^2 + 9x + 18 = 0Factor Quadratic Equation: Factor the quadratic equation. We need to find two numbers that multiply to 18 (the constant term) and add up to 9 (the coefficient of x). The numbers that satisfy these conditions are 3 and 6. So we can factor the quadratic as: (x + 3)(x + 6) = 0Solve for x: Solve for x. Set each factor equal to zero and solve for x: x + 3 = 0 or x + 6 = 0 x = -3 or x = -6

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Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Solve the quadratic by factoring.

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x^{2}+22=-9 x+4

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Answer:

x=

Write Standard Form Equation: Write the equation in standard form. $\newline$ We need to bring all terms to one side of the equation to have it in the form $ax^2 + bx + c = 0$ . $\newline$ $x^2 + 22 = -9x + 4$ $\newline$ Add $9x$ to both sides and subtract $4$ from both sides to get: $\newline$ $x^2 + 9x + 18 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $18$ (the constant term) and add up to $9$ (the coefficient of $x$ ). $\newline$ The numbers that satisfy these conditions are $3$ and $6$ . $\newline$ So we can factor the quadratic as: $\newline$ $(x + 3)(x + 6) = 0$
Solve for x: Solve for x. $\newline$ Set each factor equal to zero and solve for x: $\newline$ $x + 3 = 0$ or $x + 6 = 0$ $\newline$ $x = -3$ or $x = -6$