Question

simplifying checklist: terms that can be combined are combing there are no rounded-off decimals in any there are no fractions or decimals inside a there are no square roots in the denomina there are no square roots that can be simp any complex imaginary answers are writte 9.) $2x^2 + x = 0$ 11.) $x^2 + 8x + 7 = 0$ 13.) $-2(x + 1)^2 = -32$

Explanation:

Step1: Solve \(2x^2 + x = 0\)

Factor out \(x\): \(x(2x + 1)=0\)
Set each factor to zero: \(x = 0\) or \(2x + 1 = 0\)
Solve \(2x + 1 = 0\): \(2x=-1\), \(x = -\frac{1}{2}\)

Step2: Solve \(x^2 + 8x + 7 = 0\)

Factor the quadratic: \((x + 1)(x + 7)=0\)
Set each factor to zero: \(x + 1 = 0\) or \(x + 7 = 0\)
Solve: \(x=-1\) or \(x=-7\)

Step3: Solve \(-2(x + 1)^2 = -32\)

Divide both sides by \(-2\): \((x + 1)^2 = 16\)
Take square roots: \(x + 1=\pm4\)
Solve for \(x\): \(x=-1 + 4 = 3\) or \(x=-1 - 4=-5\)

Answer:

For \(2x^2 + x = 0\): \(x = 0\) or \(x = -\frac{1}{2}\)
For \(x^2 + 8x + 7 = 0\): \(x=-1\) or \(x=-7\)
For \(-2(x + 1)^2 = -32\): \(x = 3\) or \(x=-5\)