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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 = 29.246950766 x = 29.246950766 Simplifying x = 29.246950766Subproblem 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 = 8.753049234 x = 8.753049234 Simplifying x = 8.753049234Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.246950766, 8.753049234}
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