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Simplifying -13x + 25 = 16x2 + 120 Reorder the terms: 25 + -13x = 16x2 + 120 Reorder the terms: 25 + -13x = 120 + 16x2 Solving 25 + -13x = 120 + 16x2 Solving for variable 'x'. Reorder the terms: 25 + -120 + -13x + -16x2 = 120 + 16x2 + -120 + -16x2 Combine like terms: 25 + -120 = -95 -95 + -13x + -16x2 = 120 + 16x2 + -120 + -16x2 Reorder the terms: -95 + -13x + -16x2 = 120 + -120 + 16x2 + -16x2 Combine like terms: 120 + -120 = 0 -95 + -13x + -16x2 = 0 + 16x2 + -16x2 -95 + -13x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -95 + -13x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(95 + 13x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(95 + 13x + 16x2)' equal to zero and attempt to solve: Simplifying 95 + 13x + 16x2 = 0 Solving 95 + 13x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.9375 + 0.8125x + x2 = 0 Move the constant term to the right: Add '-5.9375' to each side of the equation. 5.9375 + 0.8125x + -5.9375 + x2 = 0 + -5.9375 Reorder the terms: 5.9375 + -5.9375 + 0.8125x + x2 = 0 + -5.9375 Combine like terms: 5.9375 + -5.9375 = 0.0000 0.0000 + 0.8125x + x2 = 0 + -5.9375 0.8125x + x2 = 0 + -5.9375 Combine like terms: 0 + -5.9375 = -5.9375 0.8125x + x2 = -5.9375 The x term is 0.8125x. Take half its coefficient (0.40625). Square it (0.1650390625) and add it to both sides. Add '0.1650390625' to each side of the equation. 0.8125x + 0.1650390625 + x2 = -5.9375 + 0.1650390625 Reorder the terms: 0.1650390625 + 0.8125x + x2 = -5.9375 + 0.1650390625 Combine like terms: -5.9375 + 0.1650390625 = -5.7724609375 0.1650390625 + 0.8125x + x2 = -5.7724609375 Factor a perfect square on the left side: (x + 0.40625)(x + 0.40625) = -5.7724609375 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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