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Simplifying 0 = x2 + x2 + -6x + -400 Reorder the terms: 0 = -400 + -6x + x2 + x2 Combine like terms: x2 + x2 = 2x2 0 = -400 + -6x + 2x2 Solving 0 = -400 + -6x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 400 = 400 400 + 6x + -2x2 = -400 + -6x + 2x2 + 400 + 6x + -2x2 Reorder the terms: 400 + 6x + -2x2 = -400 + 400 + -6x + 6x + 2x2 + -2x2 Combine like terms: -400 + 400 = 0 400 + 6x + -2x2 = 0 + -6x + 6x + 2x2 + -2x2 400 + 6x + -2x2 = -6x + 6x + 2x2 + -2x2 Combine like terms: -6x + 6x = 0 400 + 6x + -2x2 = 0 + 2x2 + -2x2 400 + 6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 400 + 6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(200 + 3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(200 + 3x + -1x2)' equal to zero and attempt to solve: Simplifying 200 + 3x + -1x2 = 0 Solving 200 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -200 + -3x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + -3x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -3x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -3x + x2 = 0 + 200 -3x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -3x + x2 = 200 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 200 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 200 + 2.25 Combine like terms: 200 + 2.25 = 202.25 2.25 + -3x + x2 = 202.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 202.25 Calculate the square root of the right side: 14.221462653 Break this problem into two subproblems by setting (x + -1.5) equal to 14.221462653 and -14.221462653.Subproblem 1
x + -1.5 = 14.221462653 Simplifying x + -1.5 = 14.221462653 Reorder the terms: -1.5 + x = 14.221462653 Solving -1.5 + x = 14.221462653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 14.221462653 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 14.221462653 + 1.5 x = 14.221462653 + 1.5 Combine like terms: 14.221462653 + 1.5 = 15.721462653 x = 15.721462653 Simplifying x = 15.721462653Subproblem 2
x + -1.5 = -14.221462653 Simplifying x + -1.5 = -14.221462653 Reorder the terms: -1.5 + x = -14.221462653 Solving -1.5 + x = -14.221462653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -14.221462653 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -14.221462653 + 1.5 x = -14.221462653 + 1.5 Combine like terms: -14.221462653 + 1.5 = -12.721462653 x = -12.721462653 Simplifying x = -12.721462653Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.721462653, -12.721462653}Solution
x = {15.721462653, -12.721462653}
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