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Simplifying x2 + 15x + 8 = 0 Reorder the terms: 8 + 15x + x2 = 0 Solving 8 + 15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 15x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 15x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 15x + x2 = 0 + -8 15x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 15x + x2 = -8 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 = -8 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -8 + 56.25 Combine like terms: -8 + 56.25 = 48.25 56.25 + 15x + x2 = 48.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + 7.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + 7.5 = 6.946221995 Simplifying x + 7.5 = 6.946221995 Reorder the terms: 7.5 + x = 6.946221995 Solving 7.5 + x = 6.946221995 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 = 6.946221995 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 6.946221995 + -7.5 x = 6.946221995 + -7.5 Combine like terms: 6.946221995 + -7.5 = -0.553778005 x = -0.553778005 Simplifying x = -0.553778005Subproblem 2
x + 7.5 = -6.946221995 Simplifying x + 7.5 = -6.946221995 Reorder the terms: 7.5 + x = -6.946221995 Solving 7.5 + x = -6.946221995 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 = -6.946221995 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -6.946221995 + -7.5 x = -6.946221995 + -7.5 Combine like terms: -6.946221995 + -7.5 = -14.446221995 x = -14.446221995 Simplifying x = -14.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.553778005, -14.446221995}
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