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Simplifying 4x2 + -10x + -200 = 0 Reorder the terms: -200 + -10x + 4x2 = 0 Solving -200 + -10x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-100 + -5x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-100 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying -100 + -5x + 2x2 = 0 Solving -100 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -50 + -2.5x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -2.5x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -2.5x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -2.5x + x2 = 0 + 50 -2.5x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -2.5x + x2 = 50 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 50 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 50 + 1.5625 Combine like terms: 50 + 1.5625 = 51.5625 1.5625 + -2.5x + x2 = 51.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 51.5625 Calculate the square root of the right side: 7.180703308 Break this problem into two subproblems by setting (x + -1.25) equal to 7.180703308 and -7.180703308.Subproblem 1
x + -1.25 = 7.180703308 Simplifying x + -1.25 = 7.180703308 Reorder the terms: -1.25 + x = 7.180703308 Solving -1.25 + x = 7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 7.180703308 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 7.180703308 + 1.25 x = 7.180703308 + 1.25 Combine like terms: 7.180703308 + 1.25 = 8.430703308 x = 8.430703308 Simplifying x = 8.430703308Subproblem 2
x + -1.25 = -7.180703308 Simplifying x + -1.25 = -7.180703308 Reorder the terms: -1.25 + x = -7.180703308 Solving -1.25 + x = -7.180703308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -7.180703308 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -7.180703308 + 1.25 x = -7.180703308 + 1.25 Combine like terms: -7.180703308 + 1.25 = -5.930703308 x = -5.930703308 Simplifying x = -5.930703308Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.430703308, -5.930703308}Solution
x = {8.430703308, -5.930703308}
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