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Simplifying 0 = x2 + 15x + 11 Reorder the terms: 0 = 11 + 15x + x2 Solving 0 = 11 + 15x + x2 Solving for variable 'x'. Combine like terms: 0 + -11 = -11 -11 + -15x + -1x2 = 11 + 15x + x2 + -11 + -15x + -1x2 Reorder the terms: -11 + -15x + -1x2 = 11 + -11 + 15x + -15x + x2 + -1x2 Combine like terms: 11 + -11 = 0 -11 + -15x + -1x2 = 0 + 15x + -15x + x2 + -1x2 -11 + -15x + -1x2 = 15x + -15x + x2 + -1x2 Combine like terms: 15x + -15x = 0 -11 + -15x + -1x2 = 0 + x2 + -1x2 -11 + -15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -11 + -15x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 15x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 15x + x2)' equal to zero and attempt to solve: Simplifying 11 + 15x + x2 = 0 Solving 11 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 15x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 15x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 15x + x2 = 0 + -11 15x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 15x + x2 = -11 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 = -11 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -11 + 56.25 Combine like terms: -11 + 56.25 = 45.25 56.25 + 15x + x2 = 45.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + 7.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + 7.5 = 6.726812024 Simplifying x + 7.5 = 6.726812024 Reorder the terms: 7.5 + x = 6.726812024 Solving 7.5 + x = 6.726812024 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 = 6.726812024 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 6.726812024 + -7.5 x = 6.726812024 + -7.5 Combine like terms: 6.726812024 + -7.5 = -0.773187976 x = -0.773187976 Simplifying x = -0.773187976Subproblem 2
x + 7.5 = -6.726812024 Simplifying x + 7.5 = -6.726812024 Reorder the terms: 7.5 + x = -6.726812024 Solving 7.5 + x = -6.726812024 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 = -6.726812024 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -6.726812024 + -7.5 x = -6.726812024 + -7.5 Combine like terms: -6.726812024 + -7.5 = -14.226812024 x = -14.226812024 Simplifying x = -14.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.773187976, -14.226812024}Solution
x = {-0.773187976, -14.226812024}
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