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

Set up the equation: Let's set up the equation and identify it as a quadratic in the form of (ax + b)(ax + b) + (ax + b) = 0. (7x - 10)² + (7x - 10) = 0Factor by grouping: We can factor by grouping since we have a common factor of (7x - 10). Let A = (7x - 10), then the equation becomes: A² + A = 0Factor the equation: Now we factor the left side of the equation as A(A + 1) = 0. (7x - 10)(7x - 10 + 1) = 0Simplify factors: Simplify the factors to find the roots of the equation. (7x - 10)(7x - 9) = 0Solve for x: Set each factor equal to zero and solve for x. First factor: 7x - 10 = 0 7x = 10 x = 10/7Second factor: Now solve for x using the second factor. Second factor: 7x - 9 = 0 7x = 9 x = 9/7

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Solve for all values of
x :

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

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

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Math Problems

Grade 8

Solve multi-step equations with fractional coefficients

Full solution

Q. Solve for all values of

x

\newline

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

\newline

Answer:

x=

Set up the equation: Let's set up the equation and identify it as a quadratic in the form of $(ax + b)(ax + b) + (ax + b) = 0$ . $(7x - 10)^2 + (7x - 10) = 0$
Factor by grouping: We can factor by grouping since we have a common factor of $(7x - 10)$ . Let $A = (7x - 10)$ , then the equation becomes: $A^2 + A = 0$
Factor the equation: Now we factor the left side of the equation as $A(A + 1) = 0$ . $\newline$ $(7x - 10)(7x - 10 + 1) = 0$
Simplify factors: Simplify the factors to find the roots of the equation. $\newline$ $(7x - 10)(7x - 9) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ First factor: $7x - 10 = 0$ $\newline$ $7x = 10$ $\newline$ $x = \frac{10}{7}$
Second factor: Now solve for $x$ using the second factor. $\newline$ Second factor: $7x - 9 = 0$ $\newline$ $7x = 9$ $\newline$ $x = \frac{9}{7}$