Solve for all values of x : (7x+8)^(2)-(7x+8)=0 Answer: x=

Identify Equation Structure: Let's first identify the structure of the equation. We have a quadratic equation in the form of a binomial squared minus the binomial itself equals zero. This suggests that we can factor by grouping.Factor Out Common Term: Factor out the common term (7x+8) from both parts of the equation. (7x+8)((7x+8)-1) = 0Simplify Equation: Simplify the equation by distributing the subtraction inside the parentheses. (7x+8)(7x+8-1) = 0 (7x+8)(7x+7) = 0Apply Zero Product Property: Now we have the product of two factors equal to zero. According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. So we set each factor equal to zero and solve for x. 7x+8 = 0 or 7x+7 = 0Solve for x (1st Equation): Solve the first equation for x. 7x+8 = 0 7x = -8 x = -8/7Solve for x (2nd Equation): Solve the second equation for x. 7x+7 = 0 7x = -7 x = -7/7 x = -1

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for all values of
x :

(7x+8)^(2)-(7x+8)=0
Answer:
x=

Solve for all values of $x$ : $\newline$ $(7 x+8)^{2}-(7 x+8)=0$ $\newline$ Answer: $x=$

View step-by-step help

Home

Math Problems

Algebra 2

Csc, sec, and cot of special angles

Full solution

Q. Solve for all values of

x

\newline

(7 x+8)^{2}-(7 x+8)=0

\newline

Answer:

x=

Identify Equation Structure: Let's first identify the structure of the equation. We have a quadratic equation in the form of a binomial squared minus the binomial itself equals zero. This suggests that we can factor by grouping.
Factor Out Common Term: Factor out the common term $(7x+8)$ from both parts of the equation. $\newline$ $(7x+8)((7x+8)-1) = 0$
Simplify Equation: Simplify the equation by distributing the subtraction inside the parentheses. $\newline$ $(7x+8)(7x+8-1) = 0$ $\newline$ $(7x+8)(7x+7) = 0$
Apply Zero Product Property: Now we have the product of two factors equal to zero. According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero. $\newline$ So we set each factor equal to zero and solve for $x$ . $\newline$ $7x+8 = 0$ or $7x+7 = 0$
Solve for $x$ ( $1$ st Equation): Solve the first equation for $x$ . $\newline$ $7x+8 = 0$ $\newline$ $7x = -8$ $\newline$ $x = -\frac{8}{7}$
Solve for x ( $2$ nd Equation): Solve the second equation for x. $\newline$ $7x+7 = 0$ $\newline$ $7x = -7$ $\newline$ $x = \frac{-7}{7}$ $\newline$ $x = -1$