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Simplifying 2x2 + 10x + 12 = 234 Reorder the terms: 12 + 10x + 2x2 = 234 Solving 12 + 10x + 2x2 = 234 Solving for variable 'x'. Reorder the terms: 12 + -234 + 10x + 2x2 = 234 + -234 Combine like terms: 12 + -234 = -222 -222 + 10x + 2x2 = 234 + -234 Combine like terms: 234 + -234 = 0 -222 + 10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-111 + 5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-111 + 5x + x2)' equal to zero and attempt to solve: Simplifying -111 + 5x + x2 = 0 Solving -111 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '111' to each side of the equation. -111 + 5x + 111 + x2 = 0 + 111 Reorder the terms: -111 + 111 + 5x + x2 = 0 + 111 Combine like terms: -111 + 111 = 0 0 + 5x + x2 = 0 + 111 5x + x2 = 0 + 111 Combine like terms: 0 + 111 = 111 5x + x2 = 111 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 111 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 111 + 6.25 Combine like terms: 111 + 6.25 = 117.25 6.25 + 5x + x2 = 117.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 117.25 Calculate the square root of the right side: 10.828203914 Break this problem into two subproblems by setting (x + 2.5) equal to 10.828203914 and -10.828203914.Subproblem 1
x + 2.5 = 10.828203914 Simplifying x + 2.5 = 10.828203914 Reorder the terms: 2.5 + x = 10.828203914 Solving 2.5 + x = 10.828203914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 10.828203914 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.828203914 + -2.5 x = 10.828203914 + -2.5 Combine like terms: 10.828203914 + -2.5 = 8.328203914 x = 8.328203914 Simplifying x = 8.328203914Subproblem 2
x + 2.5 = -10.828203914 Simplifying x + 2.5 = -10.828203914 Reorder the terms: 2.5 + x = -10.828203914 Solving 2.5 + x = -10.828203914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -10.828203914 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.828203914 + -2.5 x = -10.828203914 + -2.5 Combine like terms: -10.828203914 + -2.5 = -13.328203914 x = -13.328203914 Simplifying x = -13.328203914Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.328203914, -13.328203914}Solution
x = {8.328203914, -13.328203914}
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