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Simplifying 2x(4x + -3) = 7(8x + -4) Reorder the terms: 2x(-3 + 4x) = 7(8x + -4) (-3 * 2x + 4x * 2x) = 7(8x + -4) (-6x + 8x2) = 7(8x + -4) Reorder the terms: -6x + 8x2 = 7(-4 + 8x) -6x + 8x2 = (-4 * 7 + 8x * 7) -6x + 8x2 = (-28 + 56x) Solving -6x + 8x2 = -28 + 56x Solving for variable 'x'. Reorder the terms: 28 + -6x + -56x + 8x2 = -28 + 56x + 28 + -56x Combine like terms: -6x + -56x = -62x 28 + -62x + 8x2 = -28 + 56x + 28 + -56x Reorder the terms: 28 + -62x + 8x2 = -28 + 28 + 56x + -56x Combine like terms: -28 + 28 = 0 28 + -62x + 8x2 = 0 + 56x + -56x 28 + -62x + 8x2 = 56x + -56x Combine like terms: 56x + -56x = 0 28 + -62x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -31x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + -31x + 4x2)' equal to zero and attempt to solve: Simplifying 14 + -31x + 4x2 = 0 Solving 14 + -31x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.5 + -7.75x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -7.75x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -7.75x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -7.75x + x2 = 0 + -3.5 -7.75x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -7.75x + x2 = -3.5 The x term is -7.75x. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75x + 15.015625 + x2 = -3.5 + 15.015625 Reorder the terms: 15.015625 + -7.75x + x2 = -3.5 + 15.015625 Combine like terms: -3.5 + 15.015625 = 11.515625 15.015625 + -7.75x + x2 = 11.515625 Factor a perfect square on the left side: (x + -3.875)(x + -3.875) = 11.515625 Calculate the square root of the right side: 3.39346799 Break this problem into two subproblems by setting (x + -3.875) equal to 3.39346799 and -3.39346799.Subproblem 1
x + -3.875 = 3.39346799 Simplifying x + -3.875 = 3.39346799 Reorder the terms: -3.875 + x = 3.39346799 Solving -3.875 + x = 3.39346799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = 3.39346799 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 3.39346799 + 3.875 x = 3.39346799 + 3.875 Combine like terms: 3.39346799 + 3.875 = 7.26846799 x = 7.26846799 Simplifying x = 7.26846799Subproblem 2
x + -3.875 = -3.39346799 Simplifying x + -3.875 = -3.39346799 Reorder the terms: -3.875 + x = -3.39346799 Solving -3.875 + x = -3.39346799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = -3.39346799 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -3.39346799 + 3.875 x = -3.39346799 + 3.875 Combine like terms: -3.39346799 + 3.875 = 0.48153201 x = 0.48153201 Simplifying x = 0.48153201Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.26846799, 0.48153201}Solution
x = {7.26846799, 0.48153201}
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