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Simplifying x2 + -4x + -656 = 0 Reorder the terms: -656 + -4x + x2 = 0 Solving -656 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '656' to each side of the equation. -656 + -4x + 656 + x2 = 0 + 656 Reorder the terms: -656 + 656 + -4x + x2 = 0 + 656 Combine like terms: -656 + 656 = 0 0 + -4x + x2 = 0 + 656 -4x + x2 = 0 + 656 Combine like terms: 0 + 656 = 656 -4x + x2 = 656 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 656 + 4 Reorder the terms: 4 + -4x + x2 = 656 + 4 Combine like terms: 656 + 4 = 660 4 + -4x + x2 = 660 Factor a perfect square on the left side: (x + -2)(x + -2) = 660 Calculate the square root of the right side: 25.690465157 Break this problem into two subproblems by setting (x + -2) equal to 25.690465157 and -25.690465157.Subproblem 1
x + -2 = 25.690465157 Simplifying x + -2 = 25.690465157 Reorder the terms: -2 + x = 25.690465157 Solving -2 + x = 25.690465157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 25.690465157 + 2 Combine like terms: -2 + 2 = 0 0 + x = 25.690465157 + 2 x = 25.690465157 + 2 Combine like terms: 25.690465157 + 2 = 27.690465157 x = 27.690465157 Simplifying x = 27.690465157Subproblem 2
x + -2 = -25.690465157 Simplifying x + -2 = -25.690465157 Reorder the terms: -2 + x = -25.690465157 Solving -2 + x = -25.690465157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -25.690465157 + 2 Combine like terms: -2 + 2 = 0 0 + x = -25.690465157 + 2 x = -25.690465157 + 2 Combine like terms: -25.690465157 + 2 = -23.690465157 x = -23.690465157 Simplifying x = -23.690465157Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.690465157, -23.690465157}
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