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Simplifying x(x + 40) = 360 Reorder the terms: x(40 + x) = 360 (40 * x + x * x) = 360 (40x + x2) = 360 Solving 40x + x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 40x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '360' to each side of the equation. -360 + 40x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 40x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 40x + x2 = 0 + 360 40x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 40x + x2 = 360 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 = 360 + 400 Reorder the terms: 400 + 40x + x2 = 360 + 400 Combine like terms: 360 + 400 = 760 400 + 40x + x2 = 760 Factor a perfect square on the left side: (x + 20)(x + 20) = 760 Calculate the square root of the right side: 27.568097504 Break this problem into two subproblems by setting (x + 20) equal to 27.568097504 and -27.568097504.Subproblem 1
x + 20 = 27.568097504 Simplifying x + 20 = 27.568097504 Reorder the terms: 20 + x = 27.568097504 Solving 20 + x = 27.568097504 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 = 27.568097504 + -20 Combine like terms: 20 + -20 = 0 0 + x = 27.568097504 + -20 x = 27.568097504 + -20 Combine like terms: 27.568097504 + -20 = 7.568097504 x = 7.568097504 Simplifying x = 7.568097504Subproblem 2
x + 20 = -27.568097504 Simplifying x + 20 = -27.568097504 Reorder the terms: 20 + x = -27.568097504 Solving 20 + x = -27.568097504 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 = -27.568097504 + -20 Combine like terms: 20 + -20 = 0 0 + x = -27.568097504 + -20 x = -27.568097504 + -20 Combine like terms: -27.568097504 + -20 = -47.568097504 x = -47.568097504 Simplifying x = -47.568097504Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.568097504, -47.568097504}
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