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Simplifying -7x(2x + -1) = 4(2x + 1) Reorder the terms: -7x(-1 + 2x) = 4(2x + 1) (-1 * -7x + 2x * -7x) = 4(2x + 1) (7x + -14x2) = 4(2x + 1) Reorder the terms: 7x + -14x2 = 4(1 + 2x) 7x + -14x2 = (1 * 4 + 2x * 4) 7x + -14x2 = (4 + 8x) Solving 7x + -14x2 = 4 + 8x Solving for variable 'x'. Reorder the terms: -4 + 7x + -8x + -14x2 = 4 + 8x + -4 + -8x Combine like terms: 7x + -8x = -1x -4 + -1x + -14x2 = 4 + 8x + -4 + -8x Reorder the terms: -4 + -1x + -14x2 = 4 + -4 + 8x + -8x Combine like terms: 4 + -4 = 0 -4 + -1x + -14x2 = 0 + 8x + -8x -4 + -1x + -14x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -4 + -1x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + x + 14x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + x + 14x2)' equal to zero and attempt to solve: Simplifying 4 + x + 14x2 = 0 Solving 4 + x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.2857142857 + 0.07142857143x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 0.07142857143x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 0.07142857143x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 0.07142857143x + x2 = 0 + -0.2857142857 0.07142857143x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 0.07142857143x + x2 = -0.2857142857 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.07142857143x + 0.25 + x2 = -0.2857142857 + 0.25 Reorder the terms: 0.25 + 0.07142857143x + x2 = -0.2857142857 + 0.25 Combine like terms: -0.2857142857 + 0.25 = -0.0357142857 0.25 + 0.07142857143x + x2 = -0.0357142857 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.0357142857 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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