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Simplifying 6x2 = -60x + -102 Reorder the terms: 6x2 = -102 + -60x Solving 6x2 = -102 + -60x Solving for variable 'x'. Reorder the terms: 102 + 60x + 6x2 = -102 + -60x + 102 + 60x Reorder the terms: 102 + 60x + 6x2 = -102 + 102 + -60x + 60x Combine like terms: -102 + 102 = 0 102 + 60x + 6x2 = 0 + -60x + 60x 102 + 60x + 6x2 = -60x + 60x Combine like terms: -60x + 60x = 0 102 + 60x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(17 + 10x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(17 + 10x + x2)' equal to zero and attempt to solve: Simplifying 17 + 10x + x2 = 0 Solving 17 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 10x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 10x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 10x + x2 = 0 + -17 10x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 10x + x2 = -17 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -17 + 25 Reorder the terms: 25 + 10x + x2 = -17 + 25 Combine like terms: -17 + 25 = 8 25 + 10x + x2 = 8 Factor a perfect square on the left side: (x + 5)(x + 5) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + 5) equal to 2.828427125 and -2.828427125.Subproblem 1
x + 5 = 2.828427125 Simplifying x + 5 = 2.828427125 Reorder the terms: 5 + x = 2.828427125 Solving 5 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 2.828427125 + -5 Combine like terms: 5 + -5 = 0 0 + x = 2.828427125 + -5 x = 2.828427125 + -5 Combine like terms: 2.828427125 + -5 = -2.171572875 x = -2.171572875 Simplifying x = -2.171572875Subproblem 2
x + 5 = -2.828427125 Simplifying x + 5 = -2.828427125 Reorder the terms: 5 + x = -2.828427125 Solving 5 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -2.828427125 + -5 Combine like terms: 5 + -5 = 0 0 + x = -2.828427125 + -5 x = -2.828427125 + -5 Combine like terms: -2.828427125 + -5 = -7.828427125 x = -7.828427125 Simplifying x = -7.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.171572875, -7.828427125}Solution
x = {-2.171572875, -7.828427125}
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