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Simplifying x(x + 40) = 240 Reorder the terms: x(40 + x) = 240 (40 * x + x * x) = 240 (40x + x2) = 240 Solving 40x + x2 = 240 Solving for variable 'x'. Reorder the terms: -240 + 40x + x2 = 240 + -240 Combine like terms: 240 + -240 = 0 -240 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + 40x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + 40x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 40x + x2 = 0 + 240 40x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 40x + x2 = 240 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 = 240 + 400 Reorder the terms: 400 + 40x + x2 = 240 + 400 Combine like terms: 240 + 400 = 640 400 + 40x + x2 = 640 Factor a perfect square on the left side: (x + 20)(x + 20) = 640 Calculate the square root of the right side: 25.298221281 Break this problem into two subproblems by setting (x + 20) equal to 25.298221281 and -25.298221281.Subproblem 1
x + 20 = 25.298221281 Simplifying x + 20 = 25.298221281 Reorder the terms: 20 + x = 25.298221281 Solving 20 + x = 25.298221281 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 = 25.298221281 + -20 Combine like terms: 20 + -20 = 0 0 + x = 25.298221281 + -20 x = 25.298221281 + -20 Combine like terms: 25.298221281 + -20 = 5.298221281 x = 5.298221281 Simplifying x = 5.298221281Subproblem 2
x + 20 = -25.298221281 Simplifying x + 20 = -25.298221281 Reorder the terms: 20 + x = -25.298221281 Solving 20 + x = -25.298221281 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 = -25.298221281 + -20 Combine like terms: 20 + -20 = 0 0 + x = -25.298221281 + -20 x = -25.298221281 + -20 Combine like terms: -25.298221281 + -20 = -45.298221281 x = -45.298221281 Simplifying x = -45.298221281Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.298221281, -45.298221281}
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