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Simplifying 0 = 2x2 + 2x + -600 Reorder the terms: 0 = -600 + 2x + 2x2 Solving 0 = -600 + 2x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 600 = 600 600 + -2x + -2x2 = -600 + 2x + 2x2 + 600 + -2x + -2x2 Reorder the terms: 600 + -2x + -2x2 = -600 + 600 + 2x + -2x + 2x2 + -2x2 Combine like terms: -600 + 600 = 0 600 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2 600 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 600 + -2x + -2x2 = 0 + 2x2 + -2x2 600 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 600 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(300 + -1x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(300 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 300 + -1x + -1x2 = 0 Solving 300 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -300 + x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + x + x2 = 0 + 300 x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 x + x2 = 300 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 300 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 300 + 0.25 Combine like terms: 300 + 0.25 = 300.25 1.25 + x2 = 300.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 300.25 Calculate the square root of the right side: 17.327723451 Break this problem into two subproblems by setting (x + 0.5) equal to 17.327723451 and -17.327723451.Subproblem 1
x + 0.5 = 17.327723451 Simplifying x + 0.5 = 17.327723451 Reorder the terms: 0.5 + x = 17.327723451 Solving 0.5 + x = 17.327723451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 17.327723451 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 17.327723451 + -0.5 x = 17.327723451 + -0.5 Combine like terms: 17.327723451 + -0.5 = 16.827723451 x = 16.827723451 Simplifying x = 16.827723451Subproblem 2
x + 0.5 = -17.327723451 Simplifying x + 0.5 = -17.327723451 Reorder the terms: 0.5 + x = -17.327723451 Solving 0.5 + x = -17.327723451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -17.327723451 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -17.327723451 + -0.5 x = -17.327723451 + -0.5 Combine like terms: -17.327723451 + -0.5 = -17.827723451 x = -17.827723451 Simplifying x = -17.827723451Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.827723451, -17.827723451}Solution
x = {16.827723451, -17.827723451}
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