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Simplifying x2 + -33x + 70 = 0 Reorder the terms: 70 + -33x + x2 = 0 Solving 70 + -33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + -33x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + -33x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -33x + x2 = 0 + -70 -33x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 -33x + x2 = -70 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 = -70 + 272.25 Reorder the terms: 272.25 + -33x + x2 = -70 + 272.25 Combine like terms: -70 + 272.25 = 202.25 272.25 + -33x + x2 = 202.25 Factor a perfect square on the left side: (x + -16.5)(x + -16.5) = 202.25 Calculate the square root of the right side: 14.221462653 Break this problem into two subproblems by setting (x + -16.5) equal to 14.221462653 and -14.221462653.Subproblem 1
x + -16.5 = 14.221462653 Simplifying x + -16.5 = 14.221462653 Reorder the terms: -16.5 + x = 14.221462653 Solving -16.5 + x = 14.221462653 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 = 14.221462653 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = 14.221462653 + 16.5 x = 14.221462653 + 16.5 Combine like terms: 14.221462653 + 16.5 = 30.721462653 x = 30.721462653 Simplifying x = 30.721462653Subproblem 2
x + -16.5 = -14.221462653 Simplifying x + -16.5 = -14.221462653 Reorder the terms: -16.5 + x = -14.221462653 Solving -16.5 + x = -14.221462653 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 = -14.221462653 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + x = -14.221462653 + 16.5 x = -14.221462653 + 16.5 Combine like terms: -14.221462653 + 16.5 = 2.278537347 x = 2.278537347 Simplifying x = 2.278537347Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.721462653, 2.278537347}
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