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Simplifying 76 = -32x2 + 96x Reorder the terms: 76 = 96x + -32x2 Solving 76 = 96x + -32x2 Solving for variable 'x'. Reorder the terms: 76 + -96x + 32x2 = 96x + -96x + -32x2 + 32x2 Combine like terms: 96x + -96x = 0 76 + -96x + 32x2 = 0 + -32x2 + 32x2 76 + -96x + 32x2 = -32x2 + 32x2 Combine like terms: -32x2 + 32x2 = 0 76 + -96x + 32x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(19 + -24x + 8x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(19 + -24x + 8x2)' equal to zero and attempt to solve: Simplifying 19 + -24x + 8x2 = 0 Solving 19 + -24x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.375 + -3x + x2 = 0 Move the constant term to the right: Add '-2.375' to each side of the equation. 2.375 + -3x + -2.375 + x2 = 0 + -2.375 Reorder the terms: 2.375 + -2.375 + -3x + x2 = 0 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + -3x + x2 = 0 + -2.375 -3x + x2 = 0 + -2.375 Combine like terms: 0 + -2.375 = -2.375 -3x + x2 = -2.375 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -2.375 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -2.375 + 2.25 Combine like terms: -2.375 + 2.25 = -0.125 2.25 + -3x + x2 = -0.125 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -0.125 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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