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Simplifying -9x + -10x2 + 8 = 14 Reorder the terms: 8 + -9x + -10x2 = 14 Solving 8 + -9x + -10x2 = 14 Solving for variable 'x'. Reorder the terms: 8 + -14 + -9x + -10x2 = 14 + -14 Combine like terms: 8 + -14 = -6 -6 + -9x + -10x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -6 + -9x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 9x + 10x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 9x + 10x2)' equal to zero and attempt to solve: Simplifying 6 + 9x + 10x2 = 0 Solving 6 + 9x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.6 + 0.9x + x2 = 0.0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 0.9x + -0.6 + x2 = 0.0 + -0.6 Reorder the terms: 0.6 + -0.6 + 0.9x + x2 = 0.0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 0.9x + x2 = 0.0 + -0.6 0.9x + x2 = 0.0 + -0.6 Combine like terms: 0.0 + -0.6 = -0.6 0.9x + x2 = -0.6 The x term is 0.9x. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9x + 0.2025 + x2 = -0.6 + 0.2025 Reorder the terms: 0.2025 + 0.9x + x2 = -0.6 + 0.2025 Combine like terms: -0.6 + 0.2025 = -0.3975 0.2025 + 0.9x + x2 = -0.3975 Factor a perfect square on the left side: (x + 0.45)(x + 0.45) = -0.3975 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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