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Simplifying x2 + -40x = 18 Reorder the terms: -40x + x2 = 18 Solving -40x + x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + -40x + x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -40x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -40x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -40x + x2 = 0 + 18 -40x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -40x + x2 = 18 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 = 18 + 400 Reorder the terms: 400 + -40x + x2 = 18 + 400 Combine like terms: 18 + 400 = 418 400 + -40x + x2 = 418 Factor a perfect square on the left side: (x + -20)(x + -20) = 418 Calculate the square root of the right side: 20.4450483 Break this problem into two subproblems by setting (x + -20) equal to 20.4450483 and -20.4450483.Subproblem 1
x + -20 = 20.4450483 Simplifying x + -20 = 20.4450483 Reorder the terms: -20 + x = 20.4450483 Solving -20 + x = 20.4450483 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 = 20.4450483 + 20 Combine like terms: -20 + 20 = 0 0 + x = 20.4450483 + 20 x = 20.4450483 + 20 Combine like terms: 20.4450483 + 20 = 40.4450483 x = 40.4450483 Simplifying x = 40.4450483Subproblem 2
x + -20 = -20.4450483 Simplifying x + -20 = -20.4450483 Reorder the terms: -20 + x = -20.4450483 Solving -20 + x = -20.4450483 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 = -20.4450483 + 20 Combine like terms: -20 + 20 = 0 0 + x = -20.4450483 + 20 x = -20.4450483 + 20 Combine like terms: -20.4450483 + 20 = -0.4450483 x = -0.4450483 Simplifying x = -0.4450483Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.4450483, -0.4450483}
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