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Simplifying 32x2 + 28x + 32 = 0 Reorder the terms: 32 + 28x + 32x2 = 0 Solving 32 + 28x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(8 + 7x + 8x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + 7x + 8x2)' equal to zero and attempt to solve: Simplifying 8 + 7x + 8x2 = 0 Solving 8 + 7x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1 + 0.875x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.875x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 0.875x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.875x + x2 = 0 + -1 0.875x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.875x + x2 = -1 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = -1 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = -1 + 0.19140625 Combine like terms: -1 + 0.19140625 = -0.80859375 0.19140625 + 0.875x + x2 = -0.80859375 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = -0.80859375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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