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Simplifying x2 + -20x = -32 Reorder the terms: -20x + x2 = -32 Solving -20x + x2 = -32 Solving for variable 'x'. Reorder the terms: 32 + -20x + x2 = -32 + 32 Combine like terms: -32 + 32 = 0 32 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -20x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + -20x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -20x + x2 = 0 + -32 -20x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 -20x + x2 = -32 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 = -32 + 100 Reorder the terms: 100 + -20x + x2 = -32 + 100 Combine like terms: -32 + 100 = 68 100 + -20x + x2 = 68 Factor a perfect square on the left side: (x + -10)(x + -10) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (x + -10) equal to 8.246211251 and -8.246211251.Subproblem 1
x + -10 = 8.246211251 Simplifying x + -10 = 8.246211251 Reorder the terms: -10 + x = 8.246211251 Solving -10 + x = 8.246211251 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 = 8.246211251 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.246211251 + 10 x = 8.246211251 + 10 Combine like terms: 8.246211251 + 10 = 18.246211251 x = 18.246211251 Simplifying x = 18.246211251Subproblem 2
x + -10 = -8.246211251 Simplifying x + -10 = -8.246211251 Reorder the terms: -10 + x = -8.246211251 Solving -10 + x = -8.246211251 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 = -8.246211251 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.246211251 + 10 x = -8.246211251 + 10 Combine like terms: -8.246211251 + 10 = 1.753788749 x = 1.753788749 Simplifying x = 1.753788749Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.246211251, 1.753788749}
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