Solve for all values of x : (x-7)^(2)-10(x-7)=0 Answer: x=

Recognize quadratic form: Recognize the quadratic form of the equation. The given equation is in the form of a quadratic equation after expanding the squared term and distributing the -10.Factor common term: Factor the common term (x-7) from both parts of the equation. (x-7)((x-7) - 10) = 0 This simplifies to: (x-7)(x-7-10) = 0Simplify factored equation: Further simplify the factored equation. (x-7)(x-17) = 0Apply zero-product property: Apply the zero-product property. If the product of two factors is zero, then at least one of the factors must be zero. So, set each factor equal to zero and solve for x: x - 7 = 0 or x - 17 = 0Solve for x: Solve each equation for x. x - 7 = 0 => x = 7 x - 17 = 0 => x = 17

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Solve for all values of
x :

(x-7)^(2)-10(x-7)=0
Answer:
x=

Solve for all values of $x$ : $\newline$ $(x-7)^{2}-10(x-7)=0$ $\newline$ Answer: $x=$

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Math Problems

Algebra 2

Composition of linear and quadratic functions: find an equation

Full solution

Q. Solve for all values of

x

\newline

(x-7)^{2}-10(x-7)=0

\newline

Answer:

x=

Recognize quadratic form: Recognize the quadratic form of the equation. $\newline$ The given equation is in the form of a quadratic equation after expanding the squared term and distributing the $-10$ .
Factor common term: Factor the common term $(x-7)$ from both parts of the equation. $\newline$ $(x-7)((x-7) - 10) = 0$ $\newline$ This simplifies to: $\newline$ $(x-7)(x-7-10) = 0$
Simplify factored equation: Further simplify the factored equation. $\newline$ $(x-7)(x-17) = 0$
Apply zero-product property: Apply 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, set each factor equal to zero and solve for $x$ : $\newline$ $x - 7 = 0$ or $x - 17 = 0$
Solve for x: Solve each equation for x. $\newline$ $x - 7 = 0$ => $x = 7$ $\newline$ $x - 17 = 0$ => $x = 17$