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Simplifying 150 = 2x2 + 2x + -10 Reorder the terms: 150 = -10 + 2x + 2x2 Solving 150 = -10 + 2x + 2x2 Solving for variable 'x'. Combine like terms: 150 + 10 = 160 160 + -2x + -2x2 = -10 + 2x + 2x2 + 10 + -2x + -2x2 Reorder the terms: 160 + -2x + -2x2 = -10 + 10 + 2x + -2x + 2x2 + -2x2 Combine like terms: -10 + 10 = 0 160 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2 160 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 160 + -2x + -2x2 = 0 + 2x2 + -2x2 160 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 160 + -2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(80 + -1x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(80 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 80 + -1x + -1x2 = 0 Solving 80 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -80 + x + x2 = 0 Move the constant term to the right: Add '80' to each side of the equation. -80 + x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + x + x2 = 0 + 80 x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 x + x2 = 80 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 = 80 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 80 + 0.25 Combine like terms: 80 + 0.25 = 80.25 1.25 + x2 = 80.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (x + 0.5) equal to 8.958236434 and -8.958236434.Subproblem 1
x + 0.5 = 8.958236434 Simplifying x + 0.5 = 8.958236434 Reorder the terms: 0.5 + x = 8.958236434 Solving 0.5 + x = 8.958236434 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 = 8.958236434 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.958236434 + -0.5 x = 8.958236434 + -0.5 Combine like terms: 8.958236434 + -0.5 = 8.458236434 x = 8.458236434 Simplifying x = 8.458236434Subproblem 2
x + 0.5 = -8.958236434 Simplifying x + 0.5 = -8.958236434 Reorder the terms: 0.5 + x = -8.958236434 Solving 0.5 + x = -8.958236434 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 = -8.958236434 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.958236434 + -0.5 x = -8.958236434 + -0.5 Combine like terms: -8.958236434 + -0.5 = -9.458236434 x = -9.458236434 Simplifying x = -9.458236434Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.458236434, -9.458236434}Solution
x = {8.458236434, -9.458236434}
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