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Simplifying 2x2 + 18x + 10 = 88 Reorder the terms: 10 + 18x + 2x2 = 88 Solving 10 + 18x + 2x2 = 88 Solving for variable 'x'. Reorder the terms: 10 + -88 + 18x + 2x2 = 88 + -88 Combine like terms: 10 + -88 = -78 -78 + 18x + 2x2 = 88 + -88 Combine like terms: 88 + -88 = 0 -78 + 18x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-39 + 9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-39 + 9x + x2)' equal to zero and attempt to solve: Simplifying -39 + 9x + x2 = 0 Solving -39 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + 9x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + 9x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 9x + x2 = 0 + 39 9x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 9x + x2 = 39 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 = 39 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 39 + 20.25 Combine like terms: 39 + 20.25 = 59.25 20.25 + 9x + x2 = 59.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 59.25 Calculate the square root of the right side: 7.697402159 Break this problem into two subproblems by setting (x + 4.5) equal to 7.697402159 and -7.697402159.Subproblem 1
x + 4.5 = 7.697402159 Simplifying x + 4.5 = 7.697402159 Reorder the terms: 4.5 + x = 7.697402159 Solving 4.5 + x = 7.697402159 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 = 7.697402159 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 7.697402159 + -4.5 x = 7.697402159 + -4.5 Combine like terms: 7.697402159 + -4.5 = 3.197402159 x = 3.197402159 Simplifying x = 3.197402159Subproblem 2
x + 4.5 = -7.697402159 Simplifying x + 4.5 = -7.697402159 Reorder the terms: 4.5 + x = -7.697402159 Solving 4.5 + x = -7.697402159 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 = -7.697402159 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -7.697402159 + -4.5 x = -7.697402159 + -4.5 Combine like terms: -7.697402159 + -4.5 = -12.197402159 x = -12.197402159 Simplifying x = -12.197402159Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.197402159, -12.197402159}Solution
x = {3.197402159, -12.197402159}
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