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Simplifying 6x + -1 = 2(2x + 2)(4x + -3) Reorder the terms: -1 + 6x = 2(2x + 2)(4x + -3) Reorder the terms: -1 + 6x = 2(2 + 2x)(4x + -3) Reorder the terms: -1 + 6x = 2(2 + 2x)(-3 + 4x) Multiply (2 + 2x) * (-3 + 4x) -1 + 6x = 2(2(-3 + 4x) + 2x * (-3 + 4x)) -1 + 6x = 2((-3 * 2 + 4x * 2) + 2x * (-3 + 4x)) -1 + 6x = 2((-6 + 8x) + 2x * (-3 + 4x)) -1 + 6x = 2(-6 + 8x + (-3 * 2x + 4x * 2x)) -1 + 6x = 2(-6 + 8x + (-6x + 8x2)) Combine like terms: 8x + -6x = 2x -1 + 6x = 2(-6 + 2x + 8x2) -1 + 6x = (-6 * 2 + 2x * 2 + 8x2 * 2) -1 + 6x = (-12 + 4x + 16x2) Solving -1 + 6x = -12 + 4x + 16x2 Solving for variable 'x'. Reorder the terms: -1 + 12 + 6x + -4x + -16x2 = -12 + 4x + 16x2 + 12 + -4x + -16x2 Combine like terms: -1 + 12 = 11 11 + 6x + -4x + -16x2 = -12 + 4x + 16x2 + 12 + -4x + -16x2 Combine like terms: 6x + -4x = 2x 11 + 2x + -16x2 = -12 + 4x + 16x2 + 12 + -4x + -16x2 Reorder the terms: 11 + 2x + -16x2 = -12 + 12 + 4x + -4x + 16x2 + -16x2 Combine like terms: -12 + 12 = 0 11 + 2x + -16x2 = 0 + 4x + -4x + 16x2 + -16x2 11 + 2x + -16x2 = 4x + -4x + 16x2 + -16x2 Combine like terms: 4x + -4x = 0 11 + 2x + -16x2 = 0 + 16x2 + -16x2 11 + 2x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 11 + 2x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.6875 + -0.125x + x2 = 0 Move the constant term to the right: Add '0.6875' to each side of the equation. -0.6875 + -0.125x + 0.6875 + x2 = 0 + 0.6875 Reorder the terms: -0.6875 + 0.6875 + -0.125x + x2 = 0 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + -0.125x + x2 = 0 + 0.6875 -0.125x + x2 = 0 + 0.6875 Combine like terms: 0 + 0.6875 = 0.6875 -0.125x + x2 = 0.6875 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 0.6875 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 0.6875 + 0.00390625 Combine like terms: 0.6875 + 0.00390625 = 0.69140625 0.00390625 + -0.125x + x2 = 0.69140625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 0.69140625 Calculate the square root of the right side: 0.831508418 Break this problem into two subproblems by setting (x + -0.0625) equal to 0.831508418 and -0.831508418.Subproblem 1
x + -0.0625 = 0.831508418 Simplifying x + -0.0625 = 0.831508418 Reorder the terms: -0.0625 + x = 0.831508418 Solving -0.0625 + x = 0.831508418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 0.831508418 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.831508418 + 0.0625 x = 0.831508418 + 0.0625 Combine like terms: 0.831508418 + 0.0625 = 0.894008418 x = 0.894008418 Simplifying x = 0.894008418Subproblem 2
x + -0.0625 = -0.831508418 Simplifying x + -0.0625 = -0.831508418 Reorder the terms: -0.0625 + x = -0.831508418 Solving -0.0625 + x = -0.831508418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -0.831508418 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.831508418 + 0.0625 x = -0.831508418 + 0.0625 Combine like terms: -0.831508418 + 0.0625 = -0.769008418 x = -0.769008418 Simplifying x = -0.769008418Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.894008418, -0.769008418}
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