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Simplifying 9x2 + -18x + -27 = -4x Reorder the terms: -27 + -18x + 9x2 = -4x Solving -27 + -18x + 9x2 = -4x Solving for variable 'x'. Reorder the terms: -27 + -18x + 4x + 9x2 = -4x + 4x Combine like terms: -18x + 4x = -14x -27 + -14x + 9x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -27 + -14x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3 + -1.555555556x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.555555556x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -1.555555556x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.555555556x + x2 = 0 + 3 -1.555555556x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.555555556x + x2 = 3 The x term is -1.555555556x. Take half its coefficient (-0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. -1.555555556x + 0.6049382720 + x2 = 3 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556x + x2 = 3 + 0.6049382720 Combine like terms: 3 + 0.6049382720 = 3.604938272 0.6049382720 + -1.555555556x + x2 = 3.604938272 Factor a perfect square on the left side: (x + -0.777777778)(x + -0.777777778) = 3.604938272 Calculate the square root of the right side: 1.898667499 Break this problem into two subproblems by setting (x + -0.777777778) equal to 1.898667499 and -1.898667499.Subproblem 1
x + -0.777777778 = 1.898667499 Simplifying x + -0.777777778 = 1.898667499 Reorder the terms: -0.777777778 + x = 1.898667499 Solving -0.777777778 + x = 1.898667499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = 1.898667499 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = 1.898667499 + 0.777777778 x = 1.898667499 + 0.777777778 Combine like terms: 1.898667499 + 0.777777778 = 2.676445277 x = 2.676445277 Simplifying x = 2.676445277Subproblem 2
x + -0.777777778 = -1.898667499 Simplifying x + -0.777777778 = -1.898667499 Reorder the terms: -0.777777778 + x = -1.898667499 Solving -0.777777778 + x = -1.898667499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = -1.898667499 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = -1.898667499 + 0.777777778 x = -1.898667499 + 0.777777778 Combine like terms: -1.898667499 + 0.777777778 = -1.120889721 x = -1.120889721 Simplifying x = -1.120889721Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.676445277, -1.120889721}
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