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Simplifying 225 = (40 + -1x)(x) Reorder the terms for easier multiplication: 225 = x(40 + -1x) 225 = (40 * x + -1x * x) 225 = (40x + -1x2) Solving 225 = 40x + -1x2 Solving for variable 'x'. Reorder the terms: 225 + -40x + x2 = 40x + -40x + -1x2 + x2 Combine like terms: 40x + -40x = 0 225 + -40x + x2 = 0 + -1x2 + x2 225 + -40x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 225 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-225' to each side of the equation. 225 + -40x + -225 + x2 = 0 + -225 Reorder the terms: 225 + -225 + -40x + x2 = 0 + -225 Combine like terms: 225 + -225 = 0 0 + -40x + x2 = 0 + -225 -40x + x2 = 0 + -225 Combine like terms: 0 + -225 = -225 -40x + x2 = -225 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 = -225 + 400 Reorder the terms: 400 + -40x + x2 = -225 + 400 Combine like terms: -225 + 400 = 175 400 + -40x + x2 = 175 Factor a perfect square on the left side: (x + -20)(x + -20) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (x + -20) equal to 13.228756555 and -13.228756555.Subproblem 1
x + -20 = 13.228756555 Simplifying x + -20 = 13.228756555 Reorder the terms: -20 + x = 13.228756555 Solving -20 + x = 13.228756555 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 = 13.228756555 + 20 Combine like terms: -20 + 20 = 0 0 + x = 13.228756555 + 20 x = 13.228756555 + 20 Combine like terms: 13.228756555 + 20 = 33.228756555 x = 33.228756555 Simplifying x = 33.228756555Subproblem 2
x + -20 = -13.228756555 Simplifying x + -20 = -13.228756555 Reorder the terms: -20 + x = -13.228756555 Solving -20 + x = -13.228756555 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 = -13.228756555 + 20 Combine like terms: -20 + 20 = 0 0 + x = -13.228756555 + 20 x = -13.228756555 + 20 Combine like terms: -13.228756555 + 20 = 6.771243445 x = 6.771243445 Simplifying x = 6.771243445Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.228756555, 6.771243445}
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