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Simplifying -4x(-4x + 1) + 4x = -2x + -70 Reorder the terms: -4x(1 + -4x) + 4x = -2x + -70 (1 * -4x + -4x * -4x) + 4x = -2x + -70 (-4x + 16x2) + 4x = -2x + -70 Reorder the terms: -4x + 4x + 16x2 = -2x + -70 Combine like terms: -4x + 4x = 0 0 + 16x2 = -2x + -70 16x2 = -2x + -70 Reorder the terms: 16x2 = -70 + -2x Solving 16x2 = -70 + -2x Solving for variable 'x'. Reorder the terms: 70 + 2x + 16x2 = -70 + -2x + 70 + 2x Reorder the terms: 70 + 2x + 16x2 = -70 + 70 + -2x + 2x Combine like terms: -70 + 70 = 0 70 + 2x + 16x2 = 0 + -2x + 2x 70 + 2x + 16x2 = -2x + 2x Combine like terms: -2x + 2x = 0 70 + 2x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(35 + x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(35 + x + 8x2)' equal to zero and attempt to solve: Simplifying 35 + x + 8x2 = 0 Solving 35 + x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 4.375 + 0.125x + x2 = 0 Move the constant term to the right: Add '-4.375' to each side of the equation. 4.375 + 0.125x + -4.375 + x2 = 0 + -4.375 Reorder the terms: 4.375 + -4.375 + 0.125x + x2 = 0 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + 0.125x + x2 = 0 + -4.375 0.125x + x2 = 0 + -4.375 Combine like terms: 0 + -4.375 = -4.375 0.125x + x2 = -4.375 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. 0.125x + 0.25 + x2 = -4.375 + 0.25 Reorder the terms: 0.25 + 0.125x + x2 = -4.375 + 0.25 Combine like terms: -4.375 + 0.25 = -4.125 0.25 + 0.125x + x2 = -4.125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -4.125 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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