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Simplifying -4x2 + -40x + -106 = 0 Reorder the terms: -106 + -40x + -4x2 = 0 Solving -106 + -40x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(53 + 20x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(53 + 20x + 2x2)' equal to zero and attempt to solve: Simplifying 53 + 20x + 2x2 = 0 Solving 53 + 20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 26.5 + 10x + x2 = 0 Move the constant term to the right: Add '-26.5' to each side of the equation. 26.5 + 10x + -26.5 + x2 = 0 + -26.5 Reorder the terms: 26.5 + -26.5 + 10x + x2 = 0 + -26.5 Combine like terms: 26.5 + -26.5 = 0.0 0.0 + 10x + x2 = 0 + -26.5 10x + x2 = 0 + -26.5 Combine like terms: 0 + -26.5 = -26.5 10x + x2 = -26.5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -26.5 + 25 Reorder the terms: 25 + 10x + x2 = -26.5 + 25 Combine like terms: -26.5 + 25 = -1.5 25 + 10x + x2 = -1.5 Factor a perfect square on the left side: (x + 5)(x + 5) = -1.5 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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