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Simplifying x2 + 9x + 15 = 11 Reorder the terms: 15 + 9x + x2 = 11 Solving 15 + 9x + x2 = 11 Solving for variable 'x'. Reorder the terms: 15 + -11 + 9x + x2 = 11 + -11 Combine like terms: 15 + -11 = 4 4 + 9x + x2 = 11 + -11 Combine like terms: 11 + -11 = 0 4 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 9x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 9x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 9x + x2 = 0 + -4 9x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 9x + x2 = -4 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 = -4 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -4 + 20.25 Combine like terms: -4 + 20.25 = 16.25 20.25 + 9x + x2 = 16.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + 4.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + 4.5 = 4.031128874 Simplifying x + 4.5 = 4.031128874 Reorder the terms: 4.5 + x = 4.031128874 Solving 4.5 + x = 4.031128874 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 = 4.031128874 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.031128874 + -4.5 x = 4.031128874 + -4.5 Combine like terms: 4.031128874 + -4.5 = -0.468871126 x = -0.468871126 Simplifying x = -0.468871126Subproblem 2
x + 4.5 = -4.031128874 Simplifying x + 4.5 = -4.031128874 Reorder the terms: 4.5 + x = -4.031128874 Solving 4.5 + x = -4.031128874 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 = -4.031128874 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.031128874 + -4.5 x = -4.031128874 + -4.5 Combine like terms: -4.031128874 + -4.5 = -8.531128874 x = -8.531128874 Simplifying x = -8.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.468871126, -8.531128874}
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