Solve the quadratic by factoring. x^(2)-22 x+62=-6x-1 Answer: x=

Move Terms, Combine, Set Equal: First, we need to move all terms to one side of the equation to set it equal to zero. x^2 - 22x + 62 = -6x - 1 Add 6x to both sides and add 1 to both sides to get: x^2 - 22x + 6x + 62 + 1 = 0 Combine like terms: x^2 - 16x + 63 = 0Factor Quadratic Equation: Now, we need to factor the quadratic equation x^2 - 16x + 63. We are looking for two numbers that multiply to 63 and add up to -16. The numbers -7 and -9 satisfy these conditions because: -7 * -9 = 63 -7 + -9 = -16 So we can factor the quadratic as: (x - 7)(x - 9) = 0Solve for First Factor: To find the solutions, we set each factor equal to zero and solve for x. First, set the first factor equal to zero: x - 7 = 0 Add 7 to both sides: x = 7Solve for Second Factor: Now, set the second factor equal to zero: x - 9 = 0 Add 9 to both sides: x = 9

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Solve the quadratic by factoring.

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x^{2}-22 x+62=-6 x-1

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Answer:

x=

Move Terms, Combine, Set Equal: First, we need to move all terms to one side of the equation to set it equal to zero. $\newline$ $x^2 - 22x + 62 = -6x - 1$ $\newline$ Add $6x$ to both sides and add $1$ to both sides to get: $\newline$ $x^2 - 22x + 6x + 62 + 1 = 0$ $\newline$ Combine like terms: $\newline$ $x^2 - 16x + 63 = 0$
Factor Quadratic Equation: Now, we need to factor the quadratic equation $x^2 - 16x + 63$ . We are looking for two numbers that multiply to $63$ and add up to $-16$ . The numbers $-7$ and $-9$ satisfy these conditions because: $-7 \times -9 = 63$ $-7 + -9 = -16$ So we can factor the quadratic as: $(x - 7)(x - 9) = 0$
Solve for First Factor: To find the solutions, we set each factor equal to zero and solve for $x$ . $\newline$ First, set the first factor equal to zero: $\newline$ $x - 7 = 0$ $\newline$ Add $7$ to both sides: $\newline$ $x = 7$
Solve for Second Factor: Now, set the second factor equal to zero: $\newline$ $x - 9 = 0$ $\newline$ Add $9$ to both sides: $\newline$ $x = 9$