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Simplifying x + 1 = x2 + 10x + 5 Reorder the terms: 1 + x = x2 + 10x + 5 Reorder the terms: 1 + x = 5 + 10x + x2 Solving 1 + x = 5 + 10x + x2 Solving for variable 'x'. Reorder the terms: 1 + -5 + x + -10x + -1x2 = 5 + 10x + x2 + -5 + -10x + -1x2 Combine like terms: 1 + -5 = -4 -4 + x + -10x + -1x2 = 5 + 10x + x2 + -5 + -10x + -1x2 Combine like terms: x + -10x = -9x -4 + -9x + -1x2 = 5 + 10x + x2 + -5 + -10x + -1x2 Reorder the terms: -4 + -9x + -1x2 = 5 + -5 + 10x + -10x + x2 + -1x2 Combine like terms: 5 + -5 = 0 -4 + -9x + -1x2 = 0 + 10x + -10x + x2 + -1x2 -4 + -9x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 -4 + -9x + -1x2 = 0 + x2 + -1x2 -4 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4 + -9x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 9x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 9x + x2)' equal to zero and attempt to solve: Simplifying 4 + 9x + x2 = 0 Solving 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}Solution
x = {-0.468871126, -8.531128874}
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