Watson Ray
05/12/2024 · Junior High School
Solve the equation for \( x \). A. \( x(5 x-8)+8=-35 x+64 \) your choice. B. The solution is all real numbers. C. There is no solution.
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Tutor-Verified Answer
Step-by-step Solution
Solve the equation \( x(5x-8)+8=-35x+64 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x\left(5x-8\right)+8=-35x+64\)
- step1: Expand the expression:
\(5x^{2}-8x+8=-35x+64\)
- step2: Move the expression to the left side:
\(5x^{2}+27x-56=0\)
- step3: Factor the expression:
\(\left(x+7\right)\left(5x-8\right)=0\)
- step4: Separate into possible cases:
\(\begin{align}&5x-8=0\\&x+7=0\end{align}\)
- step5: Solve the equation:
\(\begin{align}&x=\frac{8}{5}\\&x=-7\end{align}\)
- step6: Rewrite:
\(x_{1}=-7,x_{2}=\frac{8}{5}\)
The solutions to the equation \(x(5x-8)+8=-35x+64\) are \(x=-7\) and \(x=\frac{8}{5}\) or \(x=1.6\).
Therefore, the solution to the equation is \(x=-7\) or \(x=1.6\), which means there are two solutions for the equation.
So, the correct answer is:
A. \(x=-7\) or \(x=1.6\)
Quick Answer
\(x=-7\) or \(x=1.6\)
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