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Simplifying x2 + -38x = 560 Reorder the terms: -38x + x2 = 560 Solving -38x + x2 = 560 Solving for variable 'x'. Reorder the terms: -560 + -38x + x2 = 560 + -560 Combine like terms: 560 + -560 = 0 -560 + -38x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '560' to each side of the equation. -560 + -38x + 560 + x2 = 0 + 560 Reorder the terms: -560 + 560 + -38x + x2 = 0 + 560 Combine like terms: -560 + 560 = 0 0 + -38x + x2 = 0 + 560 -38x + x2 = 0 + 560 Combine like terms: 0 + 560 = 560 -38x + x2 = 560 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 = 560 + 361 Reorder the terms: 361 + -38x + x2 = 560 + 361 Combine like terms: 560 + 361 = 921 361 + -38x + x2 = 921 Factor a perfect square on the left side: (x + -19)(x + -19) = 921 Calculate the square root of the right side: 30.347981811 Break this problem into two subproblems by setting (x + -19) equal to 30.347981811 and -30.347981811.Subproblem 1
x + -19 = 30.347981811 Simplifying x + -19 = 30.347981811 Reorder the terms: -19 + x = 30.347981811 Solving -19 + x = 30.347981811 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 = 30.347981811 + 19 Combine like terms: -19 + 19 = 0 0 + x = 30.347981811 + 19 x = 30.347981811 + 19 Combine like terms: 30.347981811 + 19 = 49.347981811 x = 49.347981811 Simplifying x = 49.347981811Subproblem 2
x + -19 = -30.347981811 Simplifying x + -19 = -30.347981811 Reorder the terms: -19 + x = -30.347981811 Solving -19 + x = -30.347981811 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 = -30.347981811 + 19 Combine like terms: -19 + 19 = 0 0 + x = -30.347981811 + 19 x = -30.347981811 + 19 Combine like terms: -30.347981811 + 19 = -11.347981811 x = -11.347981811 Simplifying x = -11.347981811Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.347981811, -11.347981811}
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