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Simplifying -5x2 + -8x + -13 = -3 Reorder the terms: -13 + -8x + -5x2 = -3 Solving -13 + -8x + -5x2 = -3 Solving for variable 'x'. Reorder the terms: -13 + 3 + -8x + -5x2 = -3 + 3 Combine like terms: -13 + 3 = -10 -10 + -8x + -5x2 = -3 + 3 Combine like terms: -3 + 3 = 0 -10 + -8x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 8x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 8x + 5x2)' equal to zero and attempt to solve: Simplifying 10 + 8x + 5x2 = 0 Solving 10 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + 1.6x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 1.6x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 1.6x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 1.6x + x2 = 0 + -2 1.6x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 1.6x + x2 = -2 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = -2 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = -2 + 0.64 Combine like terms: -2 + 0.64 = -1.36 0.64 + 1.6x + x2 = -1.36 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = -1.36 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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