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Simplifying (40 + -1x) * x + 255 = 0 Reorder the terms for easier multiplication: x(40 + -1x) + 255 = 0 (40 * x + -1x * x) + 255 = 0 (40x + -1x2) + 255 = 0 Reorder the terms: 255 + 40x + -1x2 = 0 Solving 255 + 40x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -255 + -40x + x2 = 0 Move the constant term to the right: Add '255' to each side of the equation. -255 + -40x + 255 + x2 = 0 + 255 Reorder the terms: -255 + 255 + -40x + x2 = 0 + 255 Combine like terms: -255 + 255 = 0 0 + -40x + x2 = 0 + 255 -40x + x2 = 0 + 255 Combine like terms: 0 + 255 = 255 -40x + x2 = 255 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 = 255 + 400 Reorder the terms: 400 + -40x + x2 = 255 + 400 Combine like terms: 255 + 400 = 655 400 + -40x + x2 = 655 Factor a perfect square on the left side: (x + -20)(x + -20) = 655 Calculate the square root of the right side: 25.592967784 Break this problem into two subproblems by setting (x + -20) equal to 25.592967784 and -25.592967784.Subproblem 1
x + -20 = 25.592967784 Simplifying x + -20 = 25.592967784 Reorder the terms: -20 + x = 25.592967784 Solving -20 + x = 25.592967784 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 = 25.592967784 + 20 Combine like terms: -20 + 20 = 0 0 + x = 25.592967784 + 20 x = 25.592967784 + 20 Combine like terms: 25.592967784 + 20 = 45.592967784 x = 45.592967784 Simplifying x = 45.592967784Subproblem 2
x + -20 = -25.592967784 Simplifying x + -20 = -25.592967784 Reorder the terms: -20 + x = -25.592967784 Solving -20 + x = -25.592967784 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 = -25.592967784 + 20 Combine like terms: -20 + 20 = 0 0 + x = -25.592967784 + 20 x = -25.592967784 + 20 Combine like terms: -25.592967784 + 20 = -5.592967784 x = -5.592967784 Simplifying x = -5.592967784Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.592967784, -5.592967784}
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