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Simplifying x2 + 15x + 9 = 0 Reorder the terms: 9 + 15x + x2 = 0 Solving 9 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 15x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 15x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 15x + x2 = 0 + -9 15x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 15x + x2 = -9 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 = -9 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -9 + 56.25 Combine like terms: -9 + 56.25 = 47.25 56.25 + 15x + x2 = 47.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (x + 7.5) equal to 6.873863542 and -6.873863542.Subproblem 1
x + 7.5 = 6.873863542 Simplifying x + 7.5 = 6.873863542 Reorder the terms: 7.5 + x = 6.873863542 Solving 7.5 + x = 6.873863542 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 = 6.873863542 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 6.873863542 + -7.5 x = 6.873863542 + -7.5 Combine like terms: 6.873863542 + -7.5 = -0.626136458 x = -0.626136458 Simplifying x = -0.626136458Subproblem 2
x + 7.5 = -6.873863542 Simplifying x + 7.5 = -6.873863542 Reorder the terms: 7.5 + x = -6.873863542 Solving 7.5 + x = -6.873863542 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 = -6.873863542 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -6.873863542 + -7.5 x = -6.873863542 + -7.5 Combine like terms: -6.873863542 + -7.5 = -14.373863542 x = -14.373863542 Simplifying x = -14.373863542Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.626136458, -14.373863542}
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