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Simplifying x2 + 33x + -304 = 0 Reorder the terms: -304 + 33x + x2 = 0 Solving -304 + 33x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '304' to each side of the equation. -304 + 33x + 304 + x2 = 0 + 304 Reorder the terms: -304 + 304 + 33x + x2 = 0 + 304 Combine like terms: -304 + 304 = 0 0 + 33x + x2 = 0 + 304 33x + x2 = 0 + 304 Combine like terms: 0 + 304 = 304 33x + x2 = 304 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 = 304 + 272.25 Reorder the terms: 272.25 + 33x + x2 = 304 + 272.25 Combine like terms: 304 + 272.25 = 576.25 272.25 + 33x + x2 = 576.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 576.25 Calculate the square root of the right side: 24.005207768 Break this problem into two subproblems by setting (x + 16.5) equal to 24.005207768 and -24.005207768.Subproblem 1
x + 16.5 = 24.005207768 Simplifying x + 16.5 = 24.005207768 Reorder the terms: 16.5 + x = 24.005207768 Solving 16.5 + x = 24.005207768 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 = 24.005207768 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 24.005207768 + -16.5 x = 24.005207768 + -16.5 Combine like terms: 24.005207768 + -16.5 = 7.505207768 x = 7.505207768 Simplifying x = 7.505207768Subproblem 2
x + 16.5 = -24.005207768 Simplifying x + 16.5 = -24.005207768 Reorder the terms: 16.5 + x = -24.005207768 Solving 16.5 + x = -24.005207768 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 = -24.005207768 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -24.005207768 + -16.5 x = -24.005207768 + -16.5 Combine like terms: -24.005207768 + -16.5 = -40.505207768 x = -40.505207768 Simplifying x = -40.505207768Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.505207768, -40.505207768}
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