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Simplifying 0 = x2 + 17x + 10 Reorder the terms: 0 = 10 + 17x + x2 Solving 0 = 10 + 17x + x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -17x + -1x2 = 10 + 17x + x2 + -10 + -17x + -1x2 Reorder the terms: -10 + -17x + -1x2 = 10 + -10 + 17x + -17x + x2 + -1x2 Combine like terms: 10 + -10 = 0 -10 + -17x + -1x2 = 0 + 17x + -17x + x2 + -1x2 -10 + -17x + -1x2 = 17x + -17x + x2 + -1x2 Combine like terms: 17x + -17x = 0 -10 + -17x + -1x2 = 0 + x2 + -1x2 -10 + -17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -10 + -17x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 17x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 17x + x2)' equal to zero and attempt to solve: Simplifying 10 + 17x + x2 = 0 Solving 10 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 17x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 17x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 17x + x2 = 0 + -10 17x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 17x + x2 = -10 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -10 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -10 + 72.25 Combine like terms: -10 + 72.25 = 62.25 72.25 + 17x + x2 = 62.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + 8.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + 8.5 = 7.889866919 Simplifying x + 8.5 = 7.889866919 Reorder the terms: 8.5 + x = 7.889866919 Solving 8.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 7.889866919 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 7.889866919 + -8.5 x = 7.889866919 + -8.5 Combine like terms: 7.889866919 + -8.5 = -0.610133081 x = -0.610133081 Simplifying x = -0.610133081Subproblem 2
x + 8.5 = -7.889866919 Simplifying x + 8.5 = -7.889866919 Reorder the terms: 8.5 + x = -7.889866919 Solving 8.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -7.889866919 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -7.889866919 + -8.5 x = -7.889866919 + -8.5 Combine like terms: -7.889866919 + -8.5 = -16.389866919 x = -16.389866919 Simplifying x = -16.389866919Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.610133081, -16.389866919}Solution
x = {-0.610133081, -16.389866919}
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