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Simplifying 4x2 + -200x + 450 = 0 Reorder the terms: 450 + -200x + 4x2 = 0 Solving 450 + -200x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(225 + -100x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(225 + -100x + 2x2)' equal to zero and attempt to solve: Simplifying 225 + -100x + 2x2 = 0 Solving 225 + -100x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 112.5 + -50x + x2 = 0 Move the constant term to the right: Add '-112.5' to each side of the equation. 112.5 + -50x + -112.5 + x2 = 0 + -112.5 Reorder the terms: 112.5 + -112.5 + -50x + x2 = 0 + -112.5 Combine like terms: 112.5 + -112.5 = 0.0 0.0 + -50x + x2 = 0 + -112.5 -50x + x2 = 0 + -112.5 Combine like terms: 0 + -112.5 = -112.5 -50x + x2 = -112.5 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -112.5 + 625 Reorder the terms: 625 + -50x + x2 = -112.5 + 625 Combine like terms: -112.5 + 625 = 512.5 625 + -50x + x2 = 512.5 Factor a perfect square on the left side: (x + -25)(x + -25) = 512.5 Calculate the square root of the right side: 22.638462845 Break this problem into two subproblems by setting (x + -25) equal to 22.638462845 and -22.638462845.Subproblem 1
x + -25 = 22.638462845 Simplifying x + -25 = 22.638462845 Reorder the terms: -25 + x = 22.638462845 Solving -25 + x = 22.638462845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 22.638462845 + 25 Combine like terms: -25 + 25 = 0 0 + x = 22.638462845 + 25 x = 22.638462845 + 25 Combine like terms: 22.638462845 + 25 = 47.638462845 x = 47.638462845 Simplifying x = 47.638462845Subproblem 2
x + -25 = -22.638462845 Simplifying x + -25 = -22.638462845 Reorder the terms: -25 + x = -22.638462845 Solving -25 + x = -22.638462845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -22.638462845 + 25 Combine like terms: -25 + 25 = 0 0 + x = -22.638462845 + 25 x = -22.638462845 + 25 Combine like terms: -22.638462845 + 25 = 2.361537155 x = 2.361537155 Simplifying x = 2.361537155Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.638462845, 2.361537155}Solution
x = {47.638462845, 2.361537155}
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