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Simplifying 2x2 + 18x + -316 = 0 Reorder the terms: -316 + 18x + 2x2 = 0 Solving -316 + 18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-158 + 9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-158 + 9x + x2)' equal to zero and attempt to solve: Simplifying -158 + 9x + x2 = 0 Solving -158 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '158' to each side of the equation. -158 + 9x + 158 + x2 = 0 + 158 Reorder the terms: -158 + 158 + 9x + x2 = 0 + 158 Combine like terms: -158 + 158 = 0 0 + 9x + x2 = 0 + 158 9x + x2 = 0 + 158 Combine like terms: 0 + 158 = 158 9x + x2 = 158 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 = 158 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 158 + 20.25 Combine like terms: 158 + 20.25 = 178.25 20.25 + 9x + x2 = 178.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 178.25 Calculate the square root of the right side: 13.351029923 Break this problem into two subproblems by setting (x + 4.5) equal to 13.351029923 and -13.351029923.Subproblem 1
x + 4.5 = 13.351029923 Simplifying x + 4.5 = 13.351029923 Reorder the terms: 4.5 + x = 13.351029923 Solving 4.5 + x = 13.351029923 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 = 13.351029923 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 13.351029923 + -4.5 x = 13.351029923 + -4.5 Combine like terms: 13.351029923 + -4.5 = 8.851029923 x = 8.851029923 Simplifying x = 8.851029923Subproblem 2
x + 4.5 = -13.351029923 Simplifying x + 4.5 = -13.351029923 Reorder the terms: 4.5 + x = -13.351029923 Solving 4.5 + x = -13.351029923 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 = -13.351029923 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -13.351029923 + -4.5 x = -13.351029923 + -4.5 Combine like terms: -13.351029923 + -4.5 = -17.851029923 x = -17.851029923 Simplifying x = -17.851029923Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.851029923, -17.851029923}Solution
x = {8.851029923, -17.851029923}
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