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Simplifying x2 + 9x + 20 = 112 Reorder the terms: 20 + 9x + x2 = 112 Solving 20 + 9x + x2 = 112 Solving for variable 'x'. Reorder the terms: 20 + -112 + 9x + x2 = 112 + -112 Combine like terms: 20 + -112 = -92 -92 + 9x + x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -92 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '92' to each side of the equation. -92 + 9x + 92 + x2 = 0 + 92 Reorder the terms: -92 + 92 + 9x + x2 = 0 + 92 Combine like terms: -92 + 92 = 0 0 + 9x + x2 = 0 + 92 9x + x2 = 0 + 92 Combine like terms: 0 + 92 = 92 9x + x2 = 92 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 = 92 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 92 + 20.25 Combine like terms: 92 + 20.25 = 112.25 20.25 + 9x + x2 = 112.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 112.25 Calculate the square root of the right side: 10.59481005 Break this problem into two subproblems by setting (x + 4.5) equal to 10.59481005 and -10.59481005.Subproblem 1
x + 4.5 = 10.59481005 Simplifying x + 4.5 = 10.59481005 Reorder the terms: 4.5 + x = 10.59481005 Solving 4.5 + x = 10.59481005 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 = 10.59481005 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 10.59481005 + -4.5 x = 10.59481005 + -4.5 Combine like terms: 10.59481005 + -4.5 = 6.09481005 x = 6.09481005 Simplifying x = 6.09481005Subproblem 2
x + 4.5 = -10.59481005 Simplifying x + 4.5 = -10.59481005 Reorder the terms: 4.5 + x = -10.59481005 Solving 4.5 + x = -10.59481005 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 = -10.59481005 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -10.59481005 + -4.5 x = -10.59481005 + -4.5 Combine like terms: -10.59481005 + -4.5 = -15.09481005 x = -15.09481005 Simplifying x = -15.09481005Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.09481005, -15.09481005}
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