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Simplifying -1x2 + 40x = 350 Reorder the terms: 40x + -1x2 = 350 Solving 40x + -1x2 = 350 Solving for variable 'x'. Reorder the terms: -350 + 40x + -1x2 = 350 + -350 Combine like terms: 350 + -350 = 0 -350 + 40x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 350 + -40x + x2 = 0 Move the constant term to the right: Add '-350' to each side of the equation. 350 + -40x + -350 + x2 = 0 + -350 Reorder the terms: 350 + -350 + -40x + x2 = 0 + -350 Combine like terms: 350 + -350 = 0 0 + -40x + x2 = 0 + -350 -40x + x2 = 0 + -350 Combine like terms: 0 + -350 = -350 -40x + x2 = -350 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 = -350 + 400 Reorder the terms: 400 + -40x + x2 = -350 + 400 Combine like terms: -350 + 400 = 50 400 + -40x + x2 = 50 Factor a perfect square on the left side: (x + -20)(x + -20) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + -20) equal to 7.071067812 and -7.071067812.Subproblem 1
x + -20 = 7.071067812 Simplifying x + -20 = 7.071067812 Reorder the terms: -20 + x = 7.071067812 Solving -20 + x = 7.071067812 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 = 7.071067812 + 20 Combine like terms: -20 + 20 = 0 0 + x = 7.071067812 + 20 x = 7.071067812 + 20 Combine like terms: 7.071067812 + 20 = 27.071067812 x = 27.071067812 Simplifying x = 27.071067812Subproblem 2
x + -20 = -7.071067812 Simplifying x + -20 = -7.071067812 Reorder the terms: -20 + x = -7.071067812 Solving -20 + x = -7.071067812 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 = -7.071067812 + 20 Combine like terms: -20 + 20 = 0 0 + x = -7.071067812 + 20 x = -7.071067812 + 20 Combine like terms: -7.071067812 + 20 = 12.928932188 x = 12.928932188 Simplifying x = 12.928932188Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.071067812, 12.928932188}
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