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Simplifying x2 + 20x + 10 = 23 Reorder the terms: 10 + 20x + x2 = 23 Solving 10 + 20x + x2 = 23 Solving for variable 'x'. Reorder the terms: 10 + -23 + 20x + x2 = 23 + -23 Combine like terms: 10 + -23 = -13 -13 + 20x + x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -13 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 20x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 20x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 20x + x2 = 0 + 13 20x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 20x + x2 = 13 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 = 13 + 100 Reorder the terms: 100 + 20x + x2 = 13 + 100 Combine like terms: 13 + 100 = 113 100 + 20x + x2 = 113 Factor a perfect square on the left side: (x + 10)(x + 10) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (x + 10) equal to 10.630145813 and -10.630145813.Subproblem 1
x + 10 = 10.630145813 Simplifying x + 10 = 10.630145813 Reorder the terms: 10 + x = 10.630145813 Solving 10 + x = 10.630145813 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 = 10.630145813 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.630145813 + -10 x = 10.630145813 + -10 Combine like terms: 10.630145813 + -10 = 0.630145813 x = 0.630145813 Simplifying x = 0.630145813Subproblem 2
x + 10 = -10.630145813 Simplifying x + 10 = -10.630145813 Reorder the terms: 10 + x = -10.630145813 Solving 10 + x = -10.630145813 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 = -10.630145813 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.630145813 + -10 x = -10.630145813 + -10 Combine like terms: -10.630145813 + -10 = -20.630145813 x = -20.630145813 Simplifying x = -20.630145813Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.630145813, -20.630145813}
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