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Simplifying 33x + x2 + -370 = 0 Reorder the terms: -370 + 33x + x2 = 0 Solving -370 + 33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '370' to each side of the equation. -370 + 33x + 370 + x2 = 0 + 370 Reorder the terms: -370 + 370 + 33x + x2 = 0 + 370 Combine like terms: -370 + 370 = 0 0 + 33x + x2 = 0 + 370 33x + x2 = 0 + 370 Combine like terms: 0 + 370 = 370 33x + x2 = 370 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 = 370 + 272.25 Reorder the terms: 272.25 + 33x + x2 = 370 + 272.25 Combine like terms: 370 + 272.25 = 642.25 272.25 + 33x + x2 = 642.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 642.25 Calculate the square root of the right side: 25.342651795 Break this problem into two subproblems by setting (x + 16.5) equal to 25.342651795 and -25.342651795.Subproblem 1
x + 16.5 = 25.342651795 Simplifying x + 16.5 = 25.342651795 Reorder the terms: 16.5 + x = 25.342651795 Solving 16.5 + x = 25.342651795 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 = 25.342651795 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 25.342651795 + -16.5 x = 25.342651795 + -16.5 Combine like terms: 25.342651795 + -16.5 = 8.842651795 x = 8.842651795 Simplifying x = 8.842651795Subproblem 2
x + 16.5 = -25.342651795 Simplifying x + 16.5 = -25.342651795 Reorder the terms: 16.5 + x = -25.342651795 Solving 16.5 + x = -25.342651795 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 = -25.342651795 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -25.342651795 + -16.5 x = -25.342651795 + -16.5 Combine like terms: -25.342651795 + -16.5 = -41.842651795 x = -41.842651795 Simplifying x = -41.842651795Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.842651795, -41.842651795}
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