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Simplifying -2x(5x + 3) + -2x = 2(4x + 6) + 2 Reorder the terms: -2x(3 + 5x) + -2x = 2(4x + 6) + 2 (3 * -2x + 5x * -2x) + -2x = 2(4x + 6) + 2 (-6x + -10x2) + -2x = 2(4x + 6) + 2 Reorder the terms: -6x + -2x + -10x2 = 2(4x + 6) + 2 Combine like terms: -6x + -2x = -8x -8x + -10x2 = 2(4x + 6) + 2 Reorder the terms: -8x + -10x2 = 2(6 + 4x) + 2 -8x + -10x2 = (6 * 2 + 4x * 2) + 2 -8x + -10x2 = (12 + 8x) + 2 Reorder the terms: -8x + -10x2 = 12 + 2 + 8x Combine like terms: 12 + 2 = 14 -8x + -10x2 = 14 + 8x Solving -8x + -10x2 = 14 + 8x Solving for variable 'x'. Reorder the terms: -14 + -8x + -8x + -10x2 = 14 + 8x + -14 + -8x Combine like terms: -8x + -8x = -16x -14 + -16x + -10x2 = 14 + 8x + -14 + -8x Reorder the terms: -14 + -16x + -10x2 = 14 + -14 + 8x + -8x Combine like terms: 14 + -14 = 0 -14 + -16x + -10x2 = 0 + 8x + -8x -14 + -16x + -10x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -14 + -16x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(7 + 8x + 5x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(7 + 8x + 5x2)' equal to zero and attempt to solve: Simplifying 7 + 8x + 5x2 = 0 Solving 7 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 1.6x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 1.6x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 1.6x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 1.6x + x2 = 0 + -1.4 1.6x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 1.6x + x2 = -1.4 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 = -1.4 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = -1.4 + 0.64 Combine like terms: -1.4 + 0.64 = -0.76 0.64 + 1.6x + x2 = -0.76 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = -0.76 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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