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Simplifying x(x + -38) = 180 Reorder the terms: x(-38 + x) = 180 (-38 * x + x * x) = 180 (-38x + x2) = 180 Solving -38x + x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -38x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -38x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -38x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -38x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -38x + x2 = 0 + 180 -38x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -38x + x2 = 180 The x term is -38x. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38x + 361 + x2 = 180 + 361 Reorder the terms: 361 + -38x + x2 = 180 + 361 Combine like terms: 180 + 361 = 541 361 + -38x + x2 = 541 Factor a perfect square on the left side: (x + -19)(x + -19) = 541 Calculate the square root of the right side: 23.259406699 Break this problem into two subproblems by setting (x + -19) equal to 23.259406699 and -23.259406699.Subproblem 1
x + -19 = 23.259406699 Simplifying x + -19 = 23.259406699 Reorder the terms: -19 + x = 23.259406699 Solving -19 + x = 23.259406699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 23.259406699 + 19 Combine like terms: -19 + 19 = 0 0 + x = 23.259406699 + 19 x = 23.259406699 + 19 Combine like terms: 23.259406699 + 19 = 42.259406699 x = 42.259406699 Simplifying x = 42.259406699Subproblem 2
x + -19 = -23.259406699 Simplifying x + -19 = -23.259406699 Reorder the terms: -19 + x = -23.259406699 Solving -19 + x = -23.259406699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = -23.259406699 + 19 Combine like terms: -19 + 19 = 0 0 + x = -23.259406699 + 19 x = -23.259406699 + 19 Combine like terms: -23.259406699 + 19 = -4.259406699 x = -4.259406699 Simplifying x = -4.259406699Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.259406699, -4.259406699}
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