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Simplifying 32x = 4x2 + 70 Reorder the terms: 32x = 70 + 4x2 Solving 32x = 70 + 4x2 Solving for variable 'x'. Reorder the terms: -70 + 32x + -4x2 = 70 + 4x2 + -70 + -4x2 Reorder the terms: -70 + 32x + -4x2 = 70 + -70 + 4x2 + -4x2 Combine like terms: 70 + -70 = 0 -70 + 32x + -4x2 = 0 + 4x2 + -4x2 -70 + 32x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -70 + 32x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + 16x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + 16x + -2x2)' equal to zero and attempt to solve: Simplifying -35 + 16x + -2x2 = 0 Solving -35 + 16x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 17.5 + -8x + x2 = 0 Move the constant term to the right: Add '-17.5' to each side of the equation. 17.5 + -8x + -17.5 + x2 = 0 + -17.5 Reorder the terms: 17.5 + -17.5 + -8x + x2 = 0 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + -8x + x2 = 0 + -17.5 -8x + x2 = 0 + -17.5 Combine like terms: 0 + -17.5 = -17.5 -8x + x2 = -17.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -17.5 + 16 Reorder the terms: 16 + -8x + x2 = -17.5 + 16 Combine like terms: -17.5 + 16 = -1.5 16 + -8x + x2 = -1.5 Factor a perfect square on the left side: (x + -4)(x + -4) = -1.5 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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