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Simplifying 18x2 + -37x + -36 = 0 Reorder the terms: -36 + -37x + 18x2 = 0 Solving -36 + -37x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -2 + -2.055555556x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.055555556x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -2.055555556x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.055555556x + x2 = 0 + 2 -2.055555556x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.055555556x + x2 = 2 The x term is -2.055555556x. Take half its coefficient (-1.027777778). Square it (1.056327161) and add it to both sides. Add '1.056327161' to each side of the equation. -2.055555556x + 1.056327161 + x2 = 2 + 1.056327161 Reorder the terms: 1.056327161 + -2.055555556x + x2 = 2 + 1.056327161 Combine like terms: 2 + 1.056327161 = 3.056327161 1.056327161 + -2.055555556x + x2 = 3.056327161 Factor a perfect square on the left side: (x + -1.027777778)(x + -1.027777778) = 3.056327161 Calculate the square root of the right side: 1.748235442 Break this problem into two subproblems by setting (x + -1.027777778) equal to 1.748235442 and -1.748235442.Subproblem 1
x + -1.027777778 = 1.748235442 Simplifying x + -1.027777778 = 1.748235442 Reorder the terms: -1.027777778 + x = 1.748235442 Solving -1.027777778 + x = 1.748235442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.027777778' to each side of the equation. -1.027777778 + 1.027777778 + x = 1.748235442 + 1.027777778 Combine like terms: -1.027777778 + 1.027777778 = 0.000000000 0.000000000 + x = 1.748235442 + 1.027777778 x = 1.748235442 + 1.027777778 Combine like terms: 1.748235442 + 1.027777778 = 2.77601322 x = 2.77601322 Simplifying x = 2.77601322Subproblem 2
x + -1.027777778 = -1.748235442 Simplifying x + -1.027777778 = -1.748235442 Reorder the terms: -1.027777778 + x = -1.748235442 Solving -1.027777778 + x = -1.748235442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.027777778' to each side of the equation. -1.027777778 + 1.027777778 + x = -1.748235442 + 1.027777778 Combine like terms: -1.027777778 + 1.027777778 = 0.000000000 0.000000000 + x = -1.748235442 + 1.027777778 x = -1.748235442 + 1.027777778 Combine like terms: -1.748235442 + 1.027777778 = -0.720457664 x = -0.720457664 Simplifying x = -0.720457664Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.77601322, -0.720457664}
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