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Simplifying -0.0063x2 + 4x = 200 Reorder the terms: 4x + -0.0063x2 = 200 Solving 4x + -0.0063x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + 4x + -0.0063x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 4x + -0.0063x2 = 0 Begin completing the square. Divide all terms by -0.0063 the coefficient of the squared term: Divide each side by '-0.0063'. 31746.03175 + -634.9206349x + x2 = 0 Move the constant term to the right: Add '-31746.03175' to each side of the equation. 31746.03175 + -634.9206349x + -31746.03175 + x2 = 0 + -31746.03175 Reorder the terms: 31746.03175 + -31746.03175 + -634.9206349x + x2 = 0 + -31746.03175 Combine like terms: 31746.03175 + -31746.03175 = 0.00000 0.00000 + -634.9206349x + x2 = 0 + -31746.03175 -634.9206349x + x2 = 0 + -31746.03175 Combine like terms: 0 + -31746.03175 = -31746.03175 -634.9206349x + x2 = -31746.03175 The x term is -634.9206349x. Take half its coefficient (-317.4603175). Square it (100781.0532) and add it to both sides. Add '100781.0532' to each side of the equation. -634.9206349x + 100781.0532 + x2 = -31746.03175 + 100781.0532 Reorder the terms: 100781.0532 + -634.9206349x + x2 = -31746.03175 + 100781.0532 Combine like terms: -31746.03175 + 100781.0532 = 69035.02145 100781.0532 + -634.9206349x + x2 = 69035.02145 Factor a perfect square on the left side: (x + -317.4603175)(x + -317.4603175) = 69035.02145 Calculate the square root of the right side: 262.745164465 Break this problem into two subproblems by setting (x + -317.4603175) equal to 262.745164465 and -262.745164465.Subproblem 1
x + -317.4603175 = 262.745164465 Simplifying x + -317.4603175 = 262.745164465 Reorder the terms: -317.4603175 + x = 262.745164465 Solving -317.4603175 + x = 262.745164465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '317.4603175' to each side of the equation. -317.4603175 + 317.4603175 + x = 262.745164465 + 317.4603175 Combine like terms: -317.4603175 + 317.4603175 = 0.0000000 0.0000000 + x = 262.745164465 + 317.4603175 x = 262.745164465 + 317.4603175 Combine like terms: 262.745164465 + 317.4603175 = 580.205481965 x = 580.205481965 Simplifying x = 580.205481965Subproblem 2
x + -317.4603175 = -262.745164465 Simplifying x + -317.4603175 = -262.745164465 Reorder the terms: -317.4603175 + x = -262.745164465 Solving -317.4603175 + x = -262.745164465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '317.4603175' to each side of the equation. -317.4603175 + 317.4603175 + x = -262.745164465 + 317.4603175 Combine like terms: -317.4603175 + 317.4603175 = 0.0000000 0.0000000 + x = -262.745164465 + 317.4603175 x = -262.745164465 + 317.4603175 Combine like terms: -262.745164465 + 317.4603175 = 54.715153035 x = 54.715153035 Simplifying x = 54.715153035Solution
The solution to the problem is based on the solutions from the subproblems. x = {580.205481965, 54.715153035}
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