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Simplifying x = 0.5 * 32x2 + 24x + 60 Multiply 0.5 * 32 x = 16x2 + 24x + 60 Reorder the terms: x = 60 + 24x + 16x2 Solving x = 60 + 24x + 16x2 Solving for variable 'x'. Reorder the terms: -60 + x + -24x + -16x2 = 60 + 24x + 16x2 + -60 + -24x + -16x2 Combine like terms: x + -24x = -23x -60 + -23x + -16x2 = 60 + 24x + 16x2 + -60 + -24x + -16x2 Reorder the terms: -60 + -23x + -16x2 = 60 + -60 + 24x + -24x + 16x2 + -16x2 Combine like terms: 60 + -60 = 0 -60 + -23x + -16x2 = 0 + 24x + -24x + 16x2 + -16x2 -60 + -23x + -16x2 = 24x + -24x + 16x2 + -16x2 Combine like terms: 24x + -24x = 0 -60 + -23x + -16x2 = 0 + 16x2 + -16x2 -60 + -23x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -60 + -23x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(60 + 23x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(60 + 23x + 16x2)' equal to zero and attempt to solve: Simplifying 60 + 23x + 16x2 = 0 Solving 60 + 23x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 3.75 + 1.4375x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 1.4375x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 1.4375x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 1.4375x + x2 = 0 + -3.75 1.4375x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 1.4375x + x2 = -3.75 The x term is 1.4375x. Take half its coefficient (0.71875). Square it (0.5166015625) and add it to both sides. Add '0.5166015625' to each side of the equation. 1.4375x + 0.5166015625 + x2 = -3.75 + 0.5166015625 Reorder the terms: 0.5166015625 + 1.4375x + x2 = -3.75 + 0.5166015625 Combine like terms: -3.75 + 0.5166015625 = -3.2333984375 0.5166015625 + 1.4375x + x2 = -3.2333984375 Factor a perfect square on the left side: (x + 0.71875)(x + 0.71875) = -3.2333984375 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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