Questions: For the equation: x^2 + 6x = -5 a.) The factored form is: b.) The solutions are:

For the equation: x^2 + 6x = -5 a.) The factored form is: b.) The solutions are:
Transcript text: For the equation: $x^{2}+6 x=-5$ a.) The factored form is: $\square$ b.) The solutions are: $\square$
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Solution

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Solution Steps

Step 1: Rewrite the equation in standard form

Start by moving the constant term to the left side of the equation: \[ x^{2} + 6x + 5 = 0 \]

Step 2: Factor the quadratic equation

Factor the quadratic equation \(x^{2} + 6x + 5 = 0\) into two binomials: \[ (x + 1)(x + 5) = 0 \]

Step 3: Solve for \(x\)

Set each factor equal to zero and solve for \(x\): \[ x + 1 = 0 \quad \Rightarrow \quad x = -1 \] \[ x + 5 = 0 \quad \Rightarrow \quad x = -5 \]

The solutions are \(x = \{-1, -5\}\).

Final Answer

a.) The factored form is: \(\boxed{(x + 1)(x + 5)}\)
b.) The solutions are: \(\boxed{x = -1, -5}\)

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