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Simplifying -4x2 + -6x = 192 Reorder the terms: -6x + -4x2 = 192 Solving -6x + -4x2 = 192 Solving for variable 'x'. Reorder the terms: -192 + -6x + -4x2 = 192 + -192 Combine like terms: 192 + -192 = 0 -192 + -6x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(96 + 3x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(96 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 96 + 3x + 2x2 = 0 Solving 96 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 48 + 1.5x + x2 = 0 Move the constant term to the right: Add '-48' to each side of the equation. 48 + 1.5x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + 1.5x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 1.5x + x2 = 0 + -48 1.5x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 1.5x + x2 = -48 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -48 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -48 + 0.5625 Combine like terms: -48 + 0.5625 = -47.4375 0.5625 + 1.5x + x2 = -47.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -47.4375 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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