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Simplifying 18x2 + 38x + -20 = 0 Reorder the terms: -20 + 38x + 18x2 = 0 Solving -20 + 38x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 19x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 19x + 9x2)' equal to zero and attempt to solve: Simplifying -10 + 19x + 9x2 = 0 Solving -10 + 19x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + 2.111111111x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 2.111111111x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 2.111111111x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 2.111111111x + x2 = 0 + 1.111111111 2.111111111x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 2.111111111x + x2 = 1.111111111 The x term is 2.111111111x. Take half its coefficient (1.055555556). Square it (1.114197532) and add it to both sides. Add '1.114197532' to each side of the equation. 2.111111111x + 1.114197532 + x2 = 1.111111111 + 1.114197532 Reorder the terms: 1.114197532 + 2.111111111x + x2 = 1.111111111 + 1.114197532 Combine like terms: 1.111111111 + 1.114197532 = 2.225308643 1.114197532 + 2.111111111x + x2 = 2.225308643 Factor a perfect square on the left side: (x + 1.055555556)(x + 1.055555556) = 2.225308643 Calculate the square root of the right side: 1.491746843 Break this problem into two subproblems by setting (x + 1.055555556) equal to 1.491746843 and -1.491746843.Subproblem 1
x + 1.055555556 = 1.491746843 Simplifying x + 1.055555556 = 1.491746843 Reorder the terms: 1.055555556 + x = 1.491746843 Solving 1.055555556 + x = 1.491746843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.055555556' to each side of the equation. 1.055555556 + -1.055555556 + x = 1.491746843 + -1.055555556 Combine like terms: 1.055555556 + -1.055555556 = 0.000000000 0.000000000 + x = 1.491746843 + -1.055555556 x = 1.491746843 + -1.055555556 Combine like terms: 1.491746843 + -1.055555556 = 0.436191287 x = 0.436191287 Simplifying x = 0.436191287Subproblem 2
x + 1.055555556 = -1.491746843 Simplifying x + 1.055555556 = -1.491746843 Reorder the terms: 1.055555556 + x = -1.491746843 Solving 1.055555556 + x = -1.491746843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.055555556' to each side of the equation. 1.055555556 + -1.055555556 + x = -1.491746843 + -1.055555556 Combine like terms: 1.055555556 + -1.055555556 = 0.000000000 0.000000000 + x = -1.491746843 + -1.055555556 x = -1.491746843 + -1.055555556 Combine like terms: -1.491746843 + -1.055555556 = -2.547302399 x = -2.547302399 Simplifying x = -2.547302399Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.436191287, -2.547302399}Solution
x = {0.436191287, -2.547302399}
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