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Simplifying 2x2 + 40x + -22500 = 0 Reorder the terms: -22500 + 40x + 2x2 = 0 Solving -22500 + 40x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11250 + 20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11250 + 20x + x2)' equal to zero and attempt to solve: Simplifying -11250 + 20x + x2 = 0 Solving -11250 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11250' to each side of the equation. -11250 + 20x + 11250 + x2 = 0 + 11250 Reorder the terms: -11250 + 11250 + 20x + x2 = 0 + 11250 Combine like terms: -11250 + 11250 = 0 0 + 20x + x2 = 0 + 11250 20x + x2 = 0 + 11250 Combine like terms: 0 + 11250 = 11250 20x + x2 = 11250 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 11250 + 100 Reorder the terms: 100 + 20x + x2 = 11250 + 100 Combine like terms: 11250 + 100 = 11350 100 + 20x + x2 = 11350 Factor a perfect square on the left side: (x + 10)(x + 10) = 11350 Calculate the square root of the right side: 106.536378763 Break this problem into two subproblems by setting (x + 10) equal to 106.536378763 and -106.536378763.Subproblem 1
x + 10 = 106.536378763 Simplifying x + 10 = 106.536378763 Reorder the terms: 10 + x = 106.536378763 Solving 10 + x = 106.536378763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 106.536378763 + -10 Combine like terms: 10 + -10 = 0 0 + x = 106.536378763 + -10 x = 106.536378763 + -10 Combine like terms: 106.536378763 + -10 = 96.536378763 x = 96.536378763 Simplifying x = 96.536378763Subproblem 2
x + 10 = -106.536378763 Simplifying x + 10 = -106.536378763 Reorder the terms: 10 + x = -106.536378763 Solving 10 + x = -106.536378763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -106.536378763 + -10 Combine like terms: 10 + -10 = 0 0 + x = -106.536378763 + -10 x = -106.536378763 + -10 Combine like terms: -106.536378763 + -10 = -116.536378763 x = -116.536378763 Simplifying x = -116.536378763Solution
The solution to the problem is based on the solutions from the subproblems. x = {96.536378763, -116.536378763}Solution
x = {96.536378763, -116.536378763}
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