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Simplifying x2 + 15x + 24 = 0 Reorder the terms: 24 + 15x + x2 = 0 Solving 24 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 15x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 15x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 15x + x2 = 0 + -24 15x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 15x + x2 = -24 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 = -24 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -24 + 56.25 Combine like terms: -24 + 56.25 = 32.25 56.25 + 15x + x2 = 32.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + 7.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x + 7.5 = 5.678908346 Simplifying x + 7.5 = 5.678908346 Reorder the terms: 7.5 + x = 5.678908346 Solving 7.5 + x = 5.678908346 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 = 5.678908346 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 5.678908346 + -7.5 x = 5.678908346 + -7.5 Combine like terms: 5.678908346 + -7.5 = -1.821091654 x = -1.821091654 Simplifying x = -1.821091654Subproblem 2
x + 7.5 = -5.678908346 Simplifying x + 7.5 = -5.678908346 Reorder the terms: 7.5 + x = -5.678908346 Solving 7.5 + x = -5.678908346 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 = -5.678908346 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -5.678908346 + -7.5 x = -5.678908346 + -7.5 Combine like terms: -5.678908346 + -7.5 = -13.178908346 x = -13.178908346 Simplifying x = -13.178908346Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.821091654, -13.178908346}
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