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Simplifying -4x + 100 = -2x * x + 100x Reorder the terms: 100 + -4x = -2x * x + 100x Multiply x * x 100 + -4x = -2x2 + 100x Reorder the terms: 100 + -4x = 100x + -2x2 Solving 100 + -4x = 100x + -2x2 Solving for variable 'x'. Combine like terms: -4x + -100x = -104x 100 + -104x + 2x2 = 100x + -2x2 + -100x + 2x2 Reorder the terms: 100 + -104x + 2x2 = 100x + -100x + -2x2 + 2x2 Combine like terms: 100x + -100x = 0 100 + -104x + 2x2 = 0 + -2x2 + 2x2 100 + -104x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 100 + -104x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(50 + -52x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(50 + -52x + x2)' equal to zero and attempt to solve: Simplifying 50 + -52x + x2 = 0 Solving 50 + -52x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-50' to each side of the equation. 50 + -52x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -52x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -52x + x2 = 0 + -50 -52x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -52x + x2 = -50 The x term is -52x. Take half its coefficient (-26). Square it (676) and add it to both sides. Add '676' to each side of the equation. -52x + 676 + x2 = -50 + 676 Reorder the terms: 676 + -52x + x2 = -50 + 676 Combine like terms: -50 + 676 = 626 676 + -52x + x2 = 626 Factor a perfect square on the left side: (x + -26)(x + -26) = 626 Calculate the square root of the right side: 25.019992006 Break this problem into two subproblems by setting (x + -26) equal to 25.019992006 and -25.019992006.Subproblem 1
x + -26 = 25.019992006 Simplifying x + -26 = 25.019992006 Reorder the terms: -26 + x = 25.019992006 Solving -26 + x = 25.019992006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = 25.019992006 + 26 Combine like terms: -26 + 26 = 0 0 + x = 25.019992006 + 26 x = 25.019992006 + 26 Combine like terms: 25.019992006 + 26 = 51.019992006 x = 51.019992006 Simplifying x = 51.019992006Subproblem 2
x + -26 = -25.019992006 Simplifying x + -26 = -25.019992006 Reorder the terms: -26 + x = -25.019992006 Solving -26 + x = -25.019992006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = -25.019992006 + 26 Combine like terms: -26 + 26 = 0 0 + x = -25.019992006 + 26 x = -25.019992006 + 26 Combine like terms: -25.019992006 + 26 = 0.980007994 x = 0.980007994 Simplifying x = 0.980007994Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.019992006, 0.980007994}Solution
x = {51.019992006, 0.980007994}
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