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Simplifying 0 = x2 + 34x + 200 Reorder the terms: 0 = 200 + 34x + x2 Solving 0 = 200 + 34x + x2 Solving for variable 'x'. Combine like terms: 0 + -200 = -200 -200 + -34x + -1x2 = 200 + 34x + x2 + -200 + -34x + -1x2 Reorder the terms: -200 + -34x + -1x2 = 200 + -200 + 34x + -34x + x2 + -1x2 Combine like terms: 200 + -200 = 0 -200 + -34x + -1x2 = 0 + 34x + -34x + x2 + -1x2 -200 + -34x + -1x2 = 34x + -34x + x2 + -1x2 Combine like terms: 34x + -34x = 0 -200 + -34x + -1x2 = 0 + x2 + -1x2 -200 + -34x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -200 + -34x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(200 + 34x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(200 + 34x + x2)' equal to zero and attempt to solve: Simplifying 200 + 34x + x2 = 0 Solving 200 + 34x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + 34x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + 34x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + 34x + x2 = 0 + -200 34x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 34x + x2 = -200 The x term is 34x. Take half its coefficient (17). Square it (289) and add it to both sides. Add '289' to each side of the equation. 34x + 289 + x2 = -200 + 289 Reorder the terms: 289 + 34x + x2 = -200 + 289 Combine like terms: -200 + 289 = 89 289 + 34x + x2 = 89 Factor a perfect square on the left side: (x + 17)(x + 17) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + 17) equal to 9.433981132 and -9.433981132.Subproblem 1
x + 17 = 9.433981132 Simplifying x + 17 = 9.433981132 Reorder the terms: 17 + x = 9.433981132 Solving 17 + x = 9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 9.433981132 + -17 Combine like terms: 17 + -17 = 0 0 + x = 9.433981132 + -17 x = 9.433981132 + -17 Combine like terms: 9.433981132 + -17 = -7.566018868 x = -7.566018868 Simplifying x = -7.566018868Subproblem 2
x + 17 = -9.433981132 Simplifying x + 17 = -9.433981132 Reorder the terms: 17 + x = -9.433981132 Solving 17 + x = -9.433981132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -9.433981132 + -17 Combine like terms: 17 + -17 = 0 0 + x = -9.433981132 + -17 x = -9.433981132 + -17 Combine like terms: -9.433981132 + -17 = -26.433981132 x = -26.433981132 Simplifying x = -26.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.566018868, -26.433981132}Solution
x = {-7.566018868, -26.433981132}
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