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Simplifying x2 + 38x + 256 = 0 Reorder the terms: 256 + 38x + x2 = 0 Solving 256 + 38x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-256' to each side of the equation. 256 + 38x + -256 + x2 = 0 + -256 Reorder the terms: 256 + -256 + 38x + x2 = 0 + -256 Combine like terms: 256 + -256 = 0 0 + 38x + x2 = 0 + -256 38x + x2 = 0 + -256 Combine like terms: 0 + -256 = -256 38x + x2 = -256 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 = -256 + 361 Reorder the terms: 361 + 38x + x2 = -256 + 361 Combine like terms: -256 + 361 = 105 361 + 38x + x2 = 105 Factor a perfect square on the left side: (x + 19)(x + 19) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + 19) equal to 10.246950766 and -10.246950766.Subproblem 1
x + 19 = 10.246950766 Simplifying x + 19 = 10.246950766 Reorder the terms: 19 + x = 10.246950766 Solving 19 + x = 10.246950766 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 = 10.246950766 + -19 Combine like terms: 19 + -19 = 0 0 + x = 10.246950766 + -19 x = 10.246950766 + -19 Combine like terms: 10.246950766 + -19 = -8.753049234 x = -8.753049234 Simplifying x = -8.753049234Subproblem 2
x + 19 = -10.246950766 Simplifying x + 19 = -10.246950766 Reorder the terms: 19 + x = -10.246950766 Solving 19 + x = -10.246950766 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 = -10.246950766 + -19 Combine like terms: 19 + -19 = 0 0 + x = -10.246950766 + -19 x = -10.246950766 + -19 Combine like terms: -10.246950766 + -19 = -29.246950766 x = -29.246950766 Simplifying x = -29.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-8.753049234, -29.246950766}
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