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Simplifying x2 + -40x + 328 = 0 Reorder the terms: 328 + -40x + x2 = 0 Solving 328 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-328' to each side of the equation. 328 + -40x + -328 + x2 = 0 + -328 Reorder the terms: 328 + -328 + -40x + x2 = 0 + -328 Combine like terms: 328 + -328 = 0 0 + -40x + x2 = 0 + -328 -40x + x2 = 0 + -328 Combine like terms: 0 + -328 = -328 -40x + x2 = -328 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -328 + 400 Reorder the terms: 400 + -40x + x2 = -328 + 400 Combine like terms: -328 + 400 = 72 400 + -40x + x2 = 72 Factor a perfect square on the left side: (x + -20)(x + -20) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + -20) equal to 8.485281374 and -8.485281374.Subproblem 1
x + -20 = 8.485281374 Simplifying x + -20 = 8.485281374 Reorder the terms: -20 + x = 8.485281374 Solving -20 + x = 8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 8.485281374 + 20 Combine like terms: -20 + 20 = 0 0 + x = 8.485281374 + 20 x = 8.485281374 + 20 Combine like terms: 8.485281374 + 20 = 28.485281374 x = 28.485281374 Simplifying x = 28.485281374Subproblem 2
x + -20 = -8.485281374 Simplifying x + -20 = -8.485281374 Reorder the terms: -20 + x = -8.485281374 Solving -20 + x = -8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -8.485281374 + 20 Combine like terms: -20 + 20 = 0 0 + x = -8.485281374 + 20 x = -8.485281374 + 20 Combine like terms: -8.485281374 + 20 = 11.514718626 x = 11.514718626 Simplifying x = 11.514718626Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.485281374, 11.514718626}
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