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Simplifying 2x2 + 110x + -900 = 0 Reorder the terms: -900 + 110x + 2x2 = 0 Solving -900 + 110x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-450 + 55x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-450 + 55x + x2)' equal to zero and attempt to solve: Simplifying -450 + 55x + x2 = 0 Solving -450 + 55x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '450' to each side of the equation. -450 + 55x + 450 + x2 = 0 + 450 Reorder the terms: -450 + 450 + 55x + x2 = 0 + 450 Combine like terms: -450 + 450 = 0 0 + 55x + x2 = 0 + 450 55x + x2 = 0 + 450 Combine like terms: 0 + 450 = 450 55x + x2 = 450 The x term is 55x. Take half its coefficient (27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. 55x + 756.25 + x2 = 450 + 756.25 Reorder the terms: 756.25 + 55x + x2 = 450 + 756.25 Combine like terms: 450 + 756.25 = 1206.25 756.25 + 55x + x2 = 1206.25 Factor a perfect square on the left side: (x + 27.5)(x + 27.5) = 1206.25 Calculate the square root of the right side: 34.731109974 Break this problem into two subproblems by setting (x + 27.5) equal to 34.731109974 and -34.731109974.Subproblem 1
x + 27.5 = 34.731109974 Simplifying x + 27.5 = 34.731109974 Reorder the terms: 27.5 + x = 34.731109974 Solving 27.5 + x = 34.731109974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = 34.731109974 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = 34.731109974 + -27.5 x = 34.731109974 + -27.5 Combine like terms: 34.731109974 + -27.5 = 7.231109974 x = 7.231109974 Simplifying x = 7.231109974Subproblem 2
x + 27.5 = -34.731109974 Simplifying x + 27.5 = -34.731109974 Reorder the terms: 27.5 + x = -34.731109974 Solving 27.5 + x = -34.731109974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27.5' to each side of the equation. 27.5 + -27.5 + x = -34.731109974 + -27.5 Combine like terms: 27.5 + -27.5 = 0.0 0.0 + x = -34.731109974 + -27.5 x = -34.731109974 + -27.5 Combine like terms: -34.731109974 + -27.5 = -62.231109974 x = -62.231109974 Simplifying x = -62.231109974Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.231109974, -62.231109974}Solution
x = {7.231109974, -62.231109974}
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