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Simplifying x2 + 20x + -116 = 0 Reorder the terms: -116 + 20x + x2 = 0 Solving -116 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '116' to each side of the equation. -116 + 20x + 116 + x2 = 0 + 116 Reorder the terms: -116 + 116 + 20x + x2 = 0 + 116 Combine like terms: -116 + 116 = 0 0 + 20x + x2 = 0 + 116 20x + x2 = 0 + 116 Combine like terms: 0 + 116 = 116 20x + x2 = 116 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 = 116 + 100 Reorder the terms: 100 + 20x + x2 = 116 + 100 Combine like terms: 116 + 100 = 216 100 + 20x + x2 = 216 Factor a perfect square on the left side: (x + 10)(x + 10) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (x + 10) equal to 14.696938457 and -14.696938457.Subproblem 1
x + 10 = 14.696938457 Simplifying x + 10 = 14.696938457 Reorder the terms: 10 + x = 14.696938457 Solving 10 + x = 14.696938457 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 = 14.696938457 + -10 Combine like terms: 10 + -10 = 0 0 + x = 14.696938457 + -10 x = 14.696938457 + -10 Combine like terms: 14.696938457 + -10 = 4.696938457 x = 4.696938457 Simplifying x = 4.696938457Subproblem 2
x + 10 = -14.696938457 Simplifying x + 10 = -14.696938457 Reorder the terms: 10 + x = -14.696938457 Solving 10 + x = -14.696938457 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 = -14.696938457 + -10 Combine like terms: 10 + -10 = 0 0 + x = -14.696938457 + -10 x = -14.696938457 + -10 Combine like terms: -14.696938457 + -10 = -24.696938457 x = -24.696938457 Simplifying x = -24.696938457Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.696938457, -24.696938457}
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