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Simplifying (2x + -2)(2x + 1) = 15 Reorder the terms: (-2 + 2x)(2x + 1) = 15 Reorder the terms: (-2 + 2x)(1 + 2x) = 15 Multiply (-2 + 2x) * (1 + 2x) (-2(1 + 2x) + 2x * (1 + 2x)) = 15 ((1 * -2 + 2x * -2) + 2x * (1 + 2x)) = 15 ((-2 + -4x) + 2x * (1 + 2x)) = 15 (-2 + -4x + (1 * 2x + 2x * 2x)) = 15 (-2 + -4x + (2x + 4x2)) = 15 Combine like terms: -4x + 2x = -2x (-2 + -2x + 4x2) = 15 Solving -2 + -2x + 4x2 = 15 Solving for variable 'x'. Reorder the terms: -2 + -15 + -2x + 4x2 = 15 + -15 Combine like terms: -2 + -15 = -17 -17 + -2x + 4x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -17 + -2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -4.25 + -0.5x + x2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -0.5x + 4.25 + x2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -0.5x + x2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -0.5x + x2 = 0 + 4.25 -0.5x + x2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -0.5x + x2 = 4.25 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 4.25 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 4.25 + 0.0625 Combine like terms: 4.25 + 0.0625 = 4.3125 0.0625 + -0.5x + x2 = 4.3125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 4.3125 Calculate the square root of the right side: 2.076655966 Break this problem into two subproblems by setting (x + -0.25) equal to 2.076655966 and -2.076655966.Subproblem 1
x + -0.25 = 2.076655966 Simplifying x + -0.25 = 2.076655966 Reorder the terms: -0.25 + x = 2.076655966 Solving -0.25 + x = 2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.076655966 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.076655966 + 0.25 x = 2.076655966 + 0.25 Combine like terms: 2.076655966 + 0.25 = 2.326655966 x = 2.326655966 Simplifying x = 2.326655966Subproblem 2
x + -0.25 = -2.076655966 Simplifying x + -0.25 = -2.076655966 Reorder the terms: -0.25 + x = -2.076655966 Solving -0.25 + x = -2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.076655966 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.076655966 + 0.25 x = -2.076655966 + 0.25 Combine like terms: -2.076655966 + 0.25 = -1.826655966 x = -1.826655966 Simplifying x = -1.826655966Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.326655966, -1.826655966}
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