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Simplifying 2x2 + -10x + -10 = x2 + 40 Reorder the terms: -10 + -10x + 2x2 = x2 + 40 Reorder the terms: -10 + -10x + 2x2 = 40 + x2 Solving -10 + -10x + 2x2 = 40 + x2 Solving for variable 'x'. Reorder the terms: -10 + -40 + -10x + 2x2 + -1x2 = 40 + x2 + -40 + -1x2 Combine like terms: -10 + -40 = -50 -50 + -10x + 2x2 + -1x2 = 40 + x2 + -40 + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -50 + -10x + 1x2 = 40 + x2 + -40 + -1x2 Reorder the terms: -50 + -10x + 1x2 = 40 + -40 + x2 + -1x2 Combine like terms: 40 + -40 = 0 -50 + -10x + 1x2 = 0 + x2 + -1x2 -50 + -10x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -50 + -10x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -10x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -10x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -10x + x2 = 0 + 50 -10x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -10x + x2 = 50 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 = 50 + 25 Reorder the terms: 25 + -10x + x2 = 50 + 25 Combine like terms: 50 + 25 = 75 25 + -10x + x2 = 75 Factor a perfect square on the left side: (x + -5)(x + -5) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + -5) equal to 8.660254038 and -8.660254038.Subproblem 1
x + -5 = 8.660254038 Simplifying x + -5 = 8.660254038 Reorder the terms: -5 + x = 8.660254038 Solving -5 + x = 8.660254038 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 = 8.660254038 + 5 Combine like terms: -5 + 5 = 0 0 + x = 8.660254038 + 5 x = 8.660254038 + 5 Combine like terms: 8.660254038 + 5 = 13.660254038 x = 13.660254038 Simplifying x = 13.660254038Subproblem 2
x + -5 = -8.660254038 Simplifying x + -5 = -8.660254038 Reorder the terms: -5 + x = -8.660254038 Solving -5 + x = -8.660254038 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 = -8.660254038 + 5 Combine like terms: -5 + 5 = 0 0 + x = -8.660254038 + 5 x = -8.660254038 + 5 Combine like terms: -8.660254038 + 5 = -3.660254038 x = -3.660254038 Simplifying x = -3.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.660254038, -3.660254038}
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