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Simplifying x2 + 38x + -361 = 0 Reorder the terms: -361 + 38x + x2 = 0 Solving -361 + 38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '361' to each side of the equation. -361 + 38x + 361 + x2 = 0 + 361 Reorder the terms: -361 + 361 + 38x + x2 = 0 + 361 Combine like terms: -361 + 361 = 0 0 + 38x + x2 = 0 + 361 38x + x2 = 0 + 361 Combine like terms: 0 + 361 = 361 38x + x2 = 361 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 = 361 + 361 Reorder the terms: 361 + 38x + x2 = 361 + 361 Combine like terms: 361 + 361 = 722 361 + 38x + x2 = 722 Factor a perfect square on the left side: (x + 19)(x + 19) = 722 Calculate the square root of the right side: 26.870057685 Break this problem into two subproblems by setting (x + 19) equal to 26.870057685 and -26.870057685.Subproblem 1
x + 19 = 26.870057685 Simplifying x + 19 = 26.870057685 Reorder the terms: 19 + x = 26.870057685 Solving 19 + x = 26.870057685 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 = 26.870057685 + -19 Combine like terms: 19 + -19 = 0 0 + x = 26.870057685 + -19 x = 26.870057685 + -19 Combine like terms: 26.870057685 + -19 = 7.870057685 x = 7.870057685 Simplifying x = 7.870057685Subproblem 2
x + 19 = -26.870057685 Simplifying x + 19 = -26.870057685 Reorder the terms: 19 + x = -26.870057685 Solving 19 + x = -26.870057685 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 = -26.870057685 + -19 Combine like terms: 19 + -19 = 0 0 + x = -26.870057685 + -19 x = -26.870057685 + -19 Combine like terms: -26.870057685 + -19 = -45.870057685 x = -45.870057685 Simplifying x = -45.870057685Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.870057685, -45.870057685}
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