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Simplifying 2x2 + -400x + 12500 = 0 Reorder the terms: 12500 + -400x + 2x2 = 0 Solving 12500 + -400x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6250 + -200x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6250 + -200x + x2)' equal to zero and attempt to solve: Simplifying 6250 + -200x + x2 = 0 Solving 6250 + -200x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-6250' to each side of the equation. 6250 + -200x + -6250 + x2 = 0 + -6250 Reorder the terms: 6250 + -6250 + -200x + x2 = 0 + -6250 Combine like terms: 6250 + -6250 = 0 0 + -200x + x2 = 0 + -6250 -200x + x2 = 0 + -6250 Combine like terms: 0 + -6250 = -6250 -200x + x2 = -6250 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -6250 + 10000 Reorder the terms: 10000 + -200x + x2 = -6250 + 10000 Combine like terms: -6250 + 10000 = 3750 10000 + -200x + x2 = 3750 Factor a perfect square on the left side: (x + -100)(x + -100) = 3750 Calculate the square root of the right side: 61.23724357 Break this problem into two subproblems by setting (x + -100) equal to 61.23724357 and -61.23724357.Subproblem 1
x + -100 = 61.23724357 Simplifying x + -100 = 61.23724357 Reorder the terms: -100 + x = 61.23724357 Solving -100 + x = 61.23724357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 61.23724357 + 100 Combine like terms: -100 + 100 = 0 0 + x = 61.23724357 + 100 x = 61.23724357 + 100 Combine like terms: 61.23724357 + 100 = 161.23724357 x = 161.23724357 Simplifying x = 161.23724357Subproblem 2
x + -100 = -61.23724357 Simplifying x + -100 = -61.23724357 Reorder the terms: -100 + x = -61.23724357 Solving -100 + x = -61.23724357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -61.23724357 + 100 Combine like terms: -100 + 100 = 0 0 + x = -61.23724357 + 100 x = -61.23724357 + 100 Combine like terms: -61.23724357 + 100 = 38.76275643 x = 38.76275643 Simplifying x = 38.76275643Solution
The solution to the problem is based on the solutions from the subproblems. x = {161.23724357, 38.76275643}Solution
x = {161.23724357, 38.76275643}
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