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Simplifying 0 = 2x2 + 29x + 25 Reorder the terms: 0 = 25 + 29x + 2x2 Solving 0 = 25 + 29x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -25 = -25 -25 + -29x + -2x2 = 25 + 29x + 2x2 + -25 + -29x + -2x2 Reorder the terms: -25 + -29x + -2x2 = 25 + -25 + 29x + -29x + 2x2 + -2x2 Combine like terms: 25 + -25 = 0 -25 + -29x + -2x2 = 0 + 29x + -29x + 2x2 + -2x2 -25 + -29x + -2x2 = 29x + -29x + 2x2 + -2x2 Combine like terms: 29x + -29x = 0 -25 + -29x + -2x2 = 0 + 2x2 + -2x2 -25 + -29x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -25 + -29x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(25 + 29x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(25 + 29x + 2x2)' equal to zero and attempt to solve: Simplifying 25 + 29x + 2x2 = 0 Solving 25 + 29x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + 14.5x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 14.5x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 14.5x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 14.5x + x2 = 0 + -12.5 14.5x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 14.5x + x2 = -12.5 The x term is 14.5x. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5x + 52.5625 + x2 = -12.5 + 52.5625 Reorder the terms: 52.5625 + 14.5x + x2 = -12.5 + 52.5625 Combine like terms: -12.5 + 52.5625 = 40.0625 52.5625 + 14.5x + x2 = 40.0625 Factor a perfect square on the left side: (x + 7.25)(x + 7.25) = 40.0625 Calculate the square root of the right side: 6.329494451 Break this problem into two subproblems by setting (x + 7.25) equal to 6.329494451 and -6.329494451.Subproblem 1
x + 7.25 = 6.329494451 Simplifying x + 7.25 = 6.329494451 Reorder the terms: 7.25 + x = 6.329494451 Solving 7.25 + x = 6.329494451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = 6.329494451 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 6.329494451 + -7.25 x = 6.329494451 + -7.25 Combine like terms: 6.329494451 + -7.25 = -0.920505549 x = -0.920505549 Simplifying x = -0.920505549Subproblem 2
x + 7.25 = -6.329494451 Simplifying x + 7.25 = -6.329494451 Reorder the terms: 7.25 + x = -6.329494451 Solving 7.25 + x = -6.329494451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = -6.329494451 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -6.329494451 + -7.25 x = -6.329494451 + -7.25 Combine like terms: -6.329494451 + -7.25 = -13.579494451 x = -13.579494451 Simplifying x = -13.579494451Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.920505549, -13.579494451}Solution
x = {-0.920505549, -13.579494451}
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