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Simplifying x2 + 15x + 33 = 0 Reorder the terms: 33 + 15x + x2 = 0 Solving 33 + 15x + 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 + 15x + -33 + x2 = 0 + -33 Reorder the terms: 33 + -33 + 15x + x2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + 15x + x2 = 0 + -33 15x + x2 = 0 + -33 Combine like terms: 0 + -33 = -33 15x + x2 = -33 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -33 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -33 + 56.25 Combine like terms: -33 + 56.25 = 23.25 56.25 + 15x + x2 = 23.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 23.25 Calculate the square root of the right side: 4.82182538 Break this problem into two subproblems by setting (x + 7.5) equal to 4.82182538 and -4.82182538.Subproblem 1
x + 7.5 = 4.82182538 Simplifying x + 7.5 = 4.82182538 Reorder the terms: 7.5 + x = 4.82182538 Solving 7.5 + x = 4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 4.82182538 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 4.82182538 + -7.5 x = 4.82182538 + -7.5 Combine like terms: 4.82182538 + -7.5 = -2.67817462 x = -2.67817462 Simplifying x = -2.67817462Subproblem 2
x + 7.5 = -4.82182538 Simplifying x + 7.5 = -4.82182538 Reorder the terms: 7.5 + x = -4.82182538 Solving 7.5 + x = -4.82182538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -4.82182538 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -4.82182538 + -7.5 x = -4.82182538 + -7.5 Combine like terms: -4.82182538 + -7.5 = -12.32182538 x = -12.32182538 Simplifying x = -12.32182538Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.67817462, -12.32182538}
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