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Simplifying -4x2 + -12x + -90 = 0 Reorder the terms: -90 + -12x + -4x2 = 0 Solving -90 + -12x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(45 + 6x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(45 + 6x + 2x2)' equal to zero and attempt to solve: Simplifying 45 + 6x + 2x2 = 0 Solving 45 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 22.5 + 3x + x2 = 0 Move the constant term to the right: Add '-22.5' to each side of the equation. 22.5 + 3x + -22.5 + x2 = 0 + -22.5 Reorder the terms: 22.5 + -22.5 + 3x + x2 = 0 + -22.5 Combine like terms: 22.5 + -22.5 = 0.0 0.0 + 3x + x2 = 0 + -22.5 3x + x2 = 0 + -22.5 Combine like terms: 0 + -22.5 = -22.5 3x + x2 = -22.5 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 = -22.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -22.5 + 2.25 Combine like terms: -22.5 + 2.25 = -20.25 2.25 + 3x + x2 = -20.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -20.25 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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