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Simplifying x2 + -20x + 28 = 0 Reorder the terms: 28 + -20x + x2 = 0 Solving 28 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -20x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -20x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -20x + x2 = 0 + -28 -20x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -20x + x2 = -28 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 = -28 + 100 Reorder the terms: 100 + -20x + x2 = -28 + 100 Combine like terms: -28 + 100 = 72 100 + -20x + x2 = 72 Factor a perfect square on the left side: (x + -10)(x + -10) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + -10) equal to 8.485281374 and -8.485281374.Subproblem 1
x + -10 = 8.485281374 Simplifying x + -10 = 8.485281374 Reorder the terms: -10 + x = 8.485281374 Solving -10 + x = 8.485281374 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 = 8.485281374 + 10 Combine like terms: -10 + 10 = 0 0 + x = 8.485281374 + 10 x = 8.485281374 + 10 Combine like terms: 8.485281374 + 10 = 18.485281374 x = 18.485281374 Simplifying x = 18.485281374Subproblem 2
x + -10 = -8.485281374 Simplifying x + -10 = -8.485281374 Reorder the terms: -10 + x = -8.485281374 Solving -10 + x = -8.485281374 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 = -8.485281374 + 10 Combine like terms: -10 + 10 = 0 0 + x = -8.485281374 + 10 x = -8.485281374 + 10 Combine like terms: -8.485281374 + 10 = 1.514718626 x = 1.514718626 Simplifying x = 1.514718626Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.485281374, 1.514718626}
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