Solve the quadratic by factoring. x^(2)-17 x+20=-6x+2 Answer: x=

Write Standard Form: 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 - 17x + 20 = -6x + 2 Add 6x to both sides and subtract 2 from both sides to get: x^2 - 17x + 6x + 20 - 2 = 0 Combine like terms: x^2 - 11x + 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 -11 (the coefficient of x). The numbers that satisfy these conditions are -9 and -2 because: -9 * -2 = 18 -9 + -2 = -11 So we can factor the quadratic as: (x - 9)(x - 2) = 0Solve for x: Solve for x. Set each factor equal to zero and solve for x: x - 9 = 0 or x - 2 = 0 x = 9 or x = 2

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Math Problems

Algebra 1

Factor quadratics with leading coefficient 1

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Q. Solve the quadratic by factoring.

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x^{2}-17 x+20=-6 x+2

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Answer:

x=

Write Standard Form: 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 $ax^2 + bx + c = 0$ . $\newline$ $x^2 - 17x + 20 = -6x + 2$ $\newline$ Add $6x$ to both sides and subtract $2$ from both sides to get: $\newline$ $x^2 - 17x + 6x + 20 - 2 = 0$ $\newline$ Combine like terms: $\newline$ $x^2 - 11x + 18 = 0$
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 $-11$ (the coefficient of $x$ ). $\newline$ The numbers that satisfy these conditions are $-9$ and $-2$ because: $\newline$ $-9 \times -2 = 18$ $\newline$ $-9 + -2 = -11$ $\newline$ So we can factor the quadratic as: $\newline$ $(x - 9)(x - 2) = 0$
Solve for x: Solve for x. $\newline$ Set each factor equal to zero and solve for x: $\newline$ $x - 9 = 0$ or $x - 2 = 0$ $\newline$ $x = 9$ or $x = 2$