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Simplifying x2 + -33x + -56 = 0 Reorder the terms: -56 + -33x + x2 = 0 Solving -56 + -33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -33x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -33x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -33x + x2 = 0 + 56 -33x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -33x + x2 = 56 The x term is -33x. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33x + 272.25 + x2 = 56 + 272.25 Reorder the terms: 272.25 + -33x + x2 = 56 + 272.25 Combine like terms: 56 + 272.25 = 328.25 272.25 + -33x + x2 = 328.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 328.25 Calculate the square root of the right side: 18.117670932 Break this problem into two subproblems by setting (x + -16.5) equal to 18.117670932 and -18.117670932.Subproblem 1
x + -16.5 = 18.117670932 Simplifying x + -16.5 = 18.117670932 Reorder the terms: -16.5 + x = 18.117670932 Solving -16.5 + x = 18.117670932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = 18.117670932 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 18.117670932 + 16.5 x = 18.117670932 + 16.5 Combine like terms: 18.117670932 + 16.5 = 34.617670932 x = 34.617670932 Simplifying x = 34.617670932Subproblem 2
x + -16.5 = -18.117670932 Simplifying x + -16.5 = -18.117670932 Reorder the terms: -16.5 + x = -18.117670932 Solving -16.5 + x = -18.117670932 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + x = -18.117670932 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -18.117670932 + 16.5 x = -18.117670932 + 16.5 Combine like terms: -18.117670932 + 16.5 = -1.617670932 x = -1.617670932 Simplifying x = -1.617670932Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.617670932, -1.617670932}
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