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Simplifying x2 + 10x + -146 = 0 Reorder the terms: -146 + 10x + x2 = 0 Solving -146 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '146' to each side of the equation. -146 + 10x + 146 + x2 = 0 + 146 Reorder the terms: -146 + 146 + 10x + x2 = 0 + 146 Combine like terms: -146 + 146 = 0 0 + 10x + x2 = 0 + 146 10x + x2 = 0 + 146 Combine like terms: 0 + 146 = 146 10x + x2 = 146 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 = 146 + 25 Reorder the terms: 25 + 10x + x2 = 146 + 25 Combine like terms: 146 + 25 = 171 25 + 10x + x2 = 171 Factor a perfect square on the left side: (x + 5)(x + 5) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (x + 5) equal to 13.076696831 and -13.076696831.Subproblem 1
x + 5 = 13.076696831 Simplifying x + 5 = 13.076696831 Reorder the terms: 5 + x = 13.076696831 Solving 5 + x = 13.076696831 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 = 13.076696831 + -5 Combine like terms: 5 + -5 = 0 0 + x = 13.076696831 + -5 x = 13.076696831 + -5 Combine like terms: 13.076696831 + -5 = 8.076696831 x = 8.076696831 Simplifying x = 8.076696831Subproblem 2
x + 5 = -13.076696831 Simplifying x + 5 = -13.076696831 Reorder the terms: 5 + x = -13.076696831 Solving 5 + x = -13.076696831 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 = -13.076696831 + -5 Combine like terms: 5 + -5 = 0 0 + x = -13.076696831 + -5 x = -13.076696831 + -5 Combine like terms: -13.076696831 + -5 = -18.076696831 x = -18.076696831 Simplifying x = -18.076696831Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.076696831, -18.076696831}
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