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Simplifying x2 + -20x + -162 = 0 Reorder the terms: -162 + -20x + x2 = 0 Solving -162 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '162' to each side of the equation. -162 + -20x + 162 + x2 = 0 + 162 Reorder the terms: -162 + 162 + -20x + x2 = 0 + 162 Combine like terms: -162 + 162 = 0 0 + -20x + x2 = 0 + 162 -20x + x2 = 0 + 162 Combine like terms: 0 + 162 = 162 -20x + x2 = 162 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 = 162 + 100 Reorder the terms: 100 + -20x + x2 = 162 + 100 Combine like terms: 162 + 100 = 262 100 + -20x + x2 = 262 Factor a perfect square on the left side: (x + -10)(x + -10) = 262 Calculate the square root of the right side: 16.186414056 Break this problem into two subproblems by setting (x + -10) equal to 16.186414056 and -16.186414056.Subproblem 1
x + -10 = 16.186414056 Simplifying x + -10 = 16.186414056 Reorder the terms: -10 + x = 16.186414056 Solving -10 + x = 16.186414056 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 = 16.186414056 + 10 Combine like terms: -10 + 10 = 0 0 + x = 16.186414056 + 10 x = 16.186414056 + 10 Combine like terms: 16.186414056 + 10 = 26.186414056 x = 26.186414056 Simplifying x = 26.186414056Subproblem 2
x + -10 = -16.186414056 Simplifying x + -10 = -16.186414056 Reorder the terms: -10 + x = -16.186414056 Solving -10 + x = -16.186414056 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 = -16.186414056 + 10 Combine like terms: -10 + 10 = 0 0 + x = -16.186414056 + 10 x = -16.186414056 + 10 Combine like terms: -16.186414056 + 10 = -6.186414056 x = -6.186414056 Simplifying x = -6.186414056Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.186414056, -6.186414056}
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