Question

question
solve the following quadratic equation for all values of x in simples
4(x + 7)^2 + 22 = 38
answer attempt 1 out of a
additional solution no solution
x =
± √
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Explanation:

Step1: Isolate the squared term

Subtract 22 from both sides of the equation \(4(x + 7)^2 + 22 = 38\).
\(4(x + 7)^2 = 38 - 22\)
\(4(x + 7)^2 = 16\)

Step2: Divide by the coefficient of the squared term

Divide both sides by 4.
\((x + 7)^2 = \frac{16}{4}\)
\((x + 7)^2 = 4\)

Step3: Take the square root of both sides

Take the square root of each side. Remember to consider both the positive and negative square roots.
\(x + 7 = \pm\sqrt{4}\)
\(x + 7 = \pm 2\)

Step4: Solve for x

Case 1: \(x + 7 = 2\)
Subtract 7 from both sides: \(x = 2 - 7\)
\(x = -5\)

Case 2: \(x + 7 = -2\)
Subtract 7 from both sides: \(x = -2 - 7\)
\(x = -9\)

Answer:

\(x = -5\) or \(x = -9\)