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Simplifying (2x + -5)(2x + -5) + -4x + -10x + 3 = 0 Reorder the terms: (-5 + 2x)(2x + -5) + -4x + -10x + 3 = 0 Reorder the terms: (-5 + 2x)(-5 + 2x) + -4x + -10x + 3 = 0 Multiply (-5 + 2x) * (-5 + 2x) (-5(-5 + 2x) + 2x * (-5 + 2x)) + -4x + -10x + 3 = 0 ((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + -4x + -10x + 3 = 0 ((25 + -10x) + 2x * (-5 + 2x)) + -4x + -10x + 3 = 0 (25 + -10x + (-5 * 2x + 2x * 2x)) + -4x + -10x + 3 = 0 (25 + -10x + (-10x + 4x2)) + -4x + -10x + 3 = 0 Combine like terms: -10x + -10x = -20x (25 + -20x + 4x2) + -4x + -10x + 3 = 0 Reorder the terms: 25 + 3 + -20x + -4x + -10x + 4x2 = 0 Combine like terms: 25 + 3 = 28 28 + -20x + -4x + -10x + 4x2 = 0 Combine like terms: -20x + -4x = -24x 28 + -24x + -10x + 4x2 = 0 Combine like terms: -24x + -10x = -34x 28 + -34x + 4x2 = 0 Solving 28 + -34x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -17x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + -17x + 2x2)' equal to zero and attempt to solve: Simplifying 14 + -17x + 2x2 = 0 Solving 14 + -17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7 + -8.5x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -8.5x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -8.5x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8.5x + x2 = 0 + -7 -8.5x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -8.5x + x2 = -7 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = -7 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -7 + 18.0625 Combine like terms: -7 + 18.0625 = 11.0625 18.0625 + -8.5x + x2 = 11.0625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 11.0625 Calculate the square root of the right side: 3.326033674 Break this problem into two subproblems by setting (x + -4.25) equal to 3.326033674 and -3.326033674.Subproblem 1
x + -4.25 = 3.326033674 Simplifying x + -4.25 = 3.326033674 Reorder the terms: -4.25 + x = 3.326033674 Solving -4.25 + x = 3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 3.326033674 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 3.326033674 + 4.25 x = 3.326033674 + 4.25 Combine like terms: 3.326033674 + 4.25 = 7.576033674 x = 7.576033674 Simplifying x = 7.576033674Subproblem 2
x + -4.25 = -3.326033674 Simplifying x + -4.25 = -3.326033674 Reorder the terms: -4.25 + x = -3.326033674 Solving -4.25 + x = -3.326033674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -3.326033674 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -3.326033674 + 4.25 x = -3.326033674 + 4.25 Combine like terms: -3.326033674 + 4.25 = 0.923966326 x = 0.923966326 Simplifying x = 0.923966326Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.576033674, 0.923966326}Solution
x = {7.576033674, 0.923966326}
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