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Simplifying (2x + -3) * 2 = (2x + -5)(2x + 5) + -2 Reorder the terms: (-3 + 2x) * 2 = (2x + -5)(2x + 5) + -2 Reorder the terms for easier multiplication: 2(-3 + 2x) = (2x + -5)(2x + 5) + -2 (-3 * 2 + 2x * 2) = (2x + -5)(2x + 5) + -2 (-6 + 4x) = (2x + -5)(2x + 5) + -2 Reorder the terms: -6 + 4x = (-5 + 2x)(2x + 5) + -2 Reorder the terms: -6 + 4x = (-5 + 2x)(5 + 2x) + -2 Multiply (-5 + 2x) * (5 + 2x) -6 + 4x = (-5(5 + 2x) + 2x * (5 + 2x)) + -2 -6 + 4x = ((5 * -5 + 2x * -5) + 2x * (5 + 2x)) + -2 -6 + 4x = ((-25 + -10x) + 2x * (5 + 2x)) + -2 -6 + 4x = (-25 + -10x + (5 * 2x + 2x * 2x)) + -2 -6 + 4x = (-25 + -10x + (10x + 4x2)) + -2 Combine like terms: -10x + 10x = 0 -6 + 4x = (-25 + 0 + 4x2) + -2 -6 + 4x = (-25 + 4x2) + -2 Reorder the terms: -6 + 4x = -25 + -2 + 4x2 Combine like terms: -25 + -2 = -27 -6 + 4x = -27 + 4x2 Solving -6 + 4x = -27 + 4x2 Solving for variable 'x'. Reorder the terms: -6 + 27 + 4x + -4x2 = -27 + 4x2 + 27 + -4x2 Combine like terms: -6 + 27 = 21 21 + 4x + -4x2 = -27 + 4x2 + 27 + -4x2 Reorder the terms: 21 + 4x + -4x2 = -27 + 27 + 4x2 + -4x2 Combine like terms: -27 + 27 = 0 21 + 4x + -4x2 = 0 + 4x2 + -4x2 21 + 4x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 21 + 4x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5.25 + -1x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + -1x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + -1x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + -1x + x2 = 0 + 5.25 -1x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 -1x + x2 = 5.25 The x term is -1x. 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. -1x + 0.25 + x2 = 5.25 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 5.25 + 0.25 Combine like terms: 5.25 + 0.25 = 5.5 0.25 + -1x + x2 = 5.5 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (x + -0.5) equal to 2.34520788 and -2.34520788.Subproblem 1
x + -0.5 = 2.34520788 Simplifying x + -0.5 = 2.34520788 Reorder the terms: -0.5 + x = 2.34520788 Solving -0.5 + x = 2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.34520788 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.34520788 + 0.5 x = 2.34520788 + 0.5 Combine like terms: 2.34520788 + 0.5 = 2.84520788 x = 2.84520788 Simplifying x = 2.84520788Subproblem 2
x + -0.5 = -2.34520788 Simplifying x + -0.5 = -2.34520788 Reorder the terms: -0.5 + x = -2.34520788 Solving -0.5 + x = -2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.34520788 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.34520788 + 0.5 x = -2.34520788 + 0.5 Combine like terms: -2.34520788 + 0.5 = -1.84520788 x = -1.84520788 Simplifying x = -1.84520788Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.84520788, -1.84520788}
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