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Simplifying (2x + -2)(2x + 1) = 13 Reorder the terms: (-2 + 2x)(2x + 1) = 13 Reorder the terms: (-2 + 2x)(1 + 2x) = 13 Multiply (-2 + 2x) * (1 + 2x) (-2(1 + 2x) + 2x * (1 + 2x)) = 13 ((1 * -2 + 2x * -2) + 2x * (1 + 2x)) = 13 ((-2 + -4x) + 2x * (1 + 2x)) = 13 (-2 + -4x + (1 * 2x + 2x * 2x)) = 13 (-2 + -4x + (2x + 4x2)) = 13 Combine like terms: -4x + 2x = -2x (-2 + -2x + 4x2) = 13 Solving -2 + -2x + 4x2 = 13 Solving for variable 'x'. Reorder the terms: -2 + -13 + -2x + 4x2 = 13 + -13 Combine like terms: -2 + -13 = -15 -15 + -2x + 4x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -15 + -2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -0.5x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -0.5x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -0.5x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -0.5x + x2 = 0 + 3.75 -0.5x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -0.5x + x2 = 3.75 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 = 3.75 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 3.75 + 0.0625 Combine like terms: 3.75 + 0.0625 = 3.8125 0.0625 + -0.5x + x2 = 3.8125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 3.8125 Calculate the square root of the right side: 1.952562419 Break this problem into two subproblems by setting (x + -0.25) equal to 1.952562419 and -1.952562419.Subproblem 1
x + -0.25 = 1.952562419 Simplifying x + -0.25 = 1.952562419 Reorder the terms: -0.25 + x = 1.952562419 Solving -0.25 + x = 1.952562419 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 = 1.952562419 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.952562419 + 0.25 x = 1.952562419 + 0.25 Combine like terms: 1.952562419 + 0.25 = 2.202562419 x = 2.202562419 Simplifying x = 2.202562419Subproblem 2
x + -0.25 = -1.952562419 Simplifying x + -0.25 = -1.952562419 Reorder the terms: -0.25 + x = -1.952562419 Solving -0.25 + x = -1.952562419 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 = -1.952562419 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.952562419 + 0.25 x = -1.952562419 + 0.25 Combine like terms: -1.952562419 + 0.25 = -1.702562419 x = -1.702562419 Simplifying x = -1.702562419Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.202562419, -1.702562419}
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