Question

What is the answer to this solution? solve for all possible values of x.

Answer 1

ANSWER

EXPLANATION

To solve this equation, first, square both sides of the equation,

$(\sqrt[]{25-3x})^2=(x-9)^2$

Simplify the square root with the exponent and expand the binomial squared on the right side of the equation,

$25-3x=x^2-18x+81$

Then, subtract 25 from both sides and add 3x to both sides,

$\begin{gathered} 25-25-3x+3x=x^2-18x+3x+81-25 \\ \\ 0=x^2-15x+56 \end{gathered}$

This is a quadratic equation that we can solve using the quadratic formula,

$\begin{gathered} if\text{ }ax^2+bc+c=0 \\ then\text{ }x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}$

In this case, the coefficients are a = 1, b = -15 and c = 56,

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