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Simplifying -10x2 + -12x = 76 Reorder the terms: -12x + -10x2 = 76 Solving -12x + -10x2 = 76 Solving for variable 'x'. Reorder the terms: -76 + -12x + -10x2 = 76 + -76 Combine like terms: 76 + -76 = 0 -76 + -12x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(38 + 6x + 5x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(38 + 6x + 5x2)' equal to zero and attempt to solve: Simplifying 38 + 6x + 5x2 = 0 Solving 38 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7.6 + 1.2x + x2 = 0 Move the constant term to the right: Add '-7.6' to each side of the equation. 7.6 + 1.2x + -7.6 + x2 = 0 + -7.6 Reorder the terms: 7.6 + -7.6 + 1.2x + x2 = 0 + -7.6 Combine like terms: 7.6 + -7.6 = 0.0 0.0 + 1.2x + x2 = 0 + -7.6 1.2x + x2 = 0 + -7.6 Combine like terms: 0 + -7.6 = -7.6 1.2x + x2 = -7.6 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = -7.6 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = -7.6 + 0.36 Combine like terms: -7.6 + 0.36 = -7.24 0.36 + 1.2x + x2 = -7.24 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = -7.24 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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