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Simplifying (x + 10)(x + 10) + -117 = 0 Reorder the terms: (10 + x)(x + 10) + -117 = 0 Reorder the terms: (10 + x)(10 + x) + -117 = 0 Multiply (10 + x) * (10 + x) (10(10 + x) + x(10 + x)) + -117 = 0 ((10 * 10 + x * 10) + x(10 + x)) + -117 = 0 ((100 + 10x) + x(10 + x)) + -117 = 0 (100 + 10x + (10 * x + x * x)) + -117 = 0 (100 + 10x + (10x + x2)) + -117 = 0 Combine like terms: 10x + 10x = 20x (100 + 20x + x2) + -117 = 0 Reorder the terms: 100 + -117 + 20x + x2 = 0 Combine like terms: 100 + -117 = -17 -17 + 20x + x2 = 0 Solving -17 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 20x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 20x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 20x + x2 = 0 + 17 20x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 20x + x2 = 17 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 17 + 100 Reorder the terms: 100 + 20x + x2 = 17 + 100 Combine like terms: 17 + 100 = 117 100 + 20x + x2 = 117 Factor a perfect square on the left side: (x + 10)(x + 10) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + 10) equal to 10.816653826 and -10.816653826.Subproblem 1
x + 10 = 10.816653826 Simplifying x + 10 = 10.816653826 Reorder the terms: 10 + x = 10.816653826 Solving 10 + x = 10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 10.816653826 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.816653826 + -10 x = 10.816653826 + -10 Combine like terms: 10.816653826 + -10 = 0.816653826 x = 0.816653826 Simplifying x = 0.816653826Subproblem 2
x + 10 = -10.816653826 Simplifying x + 10 = -10.816653826 Reorder the terms: 10 + x = -10.816653826 Solving 10 + x = -10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -10.816653826 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.816653826 + -10 x = -10.816653826 + -10 Combine like terms: -10.816653826 + -10 = -20.816653826 x = -20.816653826 Simplifying x = -20.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.816653826, -20.816653826}
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