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Simplifying 18x2 + -19x + -18 = 0 Reorder the terms: -18 + -19x + 18x2 = 0 Solving -18 + -19x + 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'. -1 + -1.055555556x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.055555556x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.055555556x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.055555556x + x2 = 0 + 1 -1.055555556x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.055555556x + x2 = 1 The x term is -1.055555556x. Take half its coefficient (-0.527777778). Square it (0.2785493830) and add it to both sides. Add '0.2785493830' to each side of the equation. -1.055555556x + 0.2785493830 + x2 = 1 + 0.2785493830 Reorder the terms: 0.2785493830 + -1.055555556x + x2 = 1 + 0.2785493830 Combine like terms: 1 + 0.2785493830 = 1.278549383 0.2785493830 + -1.055555556x + x2 = 1.278549383 Factor a perfect square on the left side: (x + -0.527777778)(x + -0.527777778) = 1.278549383 Calculate the square root of the right side: 1.13072958 Break this problem into two subproblems by setting (x + -0.527777778) equal to 1.13072958 and -1.13072958.Subproblem 1
x + -0.527777778 = 1.13072958 Simplifying x + -0.527777778 = 1.13072958 Reorder the terms: -0.527777778 + x = 1.13072958 Solving -0.527777778 + x = 1.13072958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.527777778' to each side of the equation. -0.527777778 + 0.527777778 + x = 1.13072958 + 0.527777778 Combine like terms: -0.527777778 + 0.527777778 = 0.000000000 0.000000000 + x = 1.13072958 + 0.527777778 x = 1.13072958 + 0.527777778 Combine like terms: 1.13072958 + 0.527777778 = 1.658507358 x = 1.658507358 Simplifying x = 1.658507358Subproblem 2
x + -0.527777778 = -1.13072958 Simplifying x + -0.527777778 = -1.13072958 Reorder the terms: -0.527777778 + x = -1.13072958 Solving -0.527777778 + x = -1.13072958 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.527777778' to each side of the equation. -0.527777778 + 0.527777778 + x = -1.13072958 + 0.527777778 Combine like terms: -0.527777778 + 0.527777778 = 0.000000000 0.000000000 + x = -1.13072958 + 0.527777778 x = -1.13072958 + 0.527777778 Combine like terms: -1.13072958 + 0.527777778 = -0.602951802 x = -0.602951802 Simplifying x = -0.602951802Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.658507358, -0.602951802}
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