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Simplifying x2 + 9x + -33 = 0 Reorder the terms: -33 + 9x + x2 = 0 Solving -33 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 9x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 9x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 9x + x2 = 0 + 33 9x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 9x + x2 = 33 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 33 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 33 + 20.25 Combine like terms: 33 + 20.25 = 53.25 20.25 + 9x + x2 = 53.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 53.25 Calculate the square root of the right side: 7.29725976 Break this problem into two subproblems by setting (x + 4.5) equal to 7.29725976 and -7.29725976.Subproblem 1
x + 4.5 = 7.29725976 Simplifying x + 4.5 = 7.29725976 Reorder the terms: 4.5 + x = 7.29725976 Solving 4.5 + x = 7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 7.29725976 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 7.29725976 + -4.5 x = 7.29725976 + -4.5 Combine like terms: 7.29725976 + -4.5 = 2.79725976 x = 2.79725976 Simplifying x = 2.79725976Subproblem 2
x + 4.5 = -7.29725976 Simplifying x + 4.5 = -7.29725976 Reorder the terms: 4.5 + x = -7.29725976 Solving 4.5 + x = -7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -7.29725976 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -7.29725976 + -4.5 x = -7.29725976 + -4.5 Combine like terms: -7.29725976 + -4.5 = -11.79725976 x = -11.79725976 Simplifying x = -11.79725976Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.79725976, -11.79725976}
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