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Simplifying 4x2 + -36x + -27 = 0 Reorder the terms: -27 + -36x + 4x2 = 0 Solving -27 + -36x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + -9x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + -9x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + -9x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + -9x + x2 = 0 + 6.75 -9x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 -9x + x2 = 6.75 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 = 6.75 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 6.75 + 20.25 Combine like terms: 6.75 + 20.25 = 27 20.25 + -9x + x2 = 27 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + -4.5) equal to 5.196152423 and -5.196152423.Subproblem 1
x + -4.5 = 5.196152423 Simplifying x + -4.5 = 5.196152423 Reorder the terms: -4.5 + x = 5.196152423 Solving -4.5 + x = 5.196152423 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 = 5.196152423 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.196152423 + 4.5 x = 5.196152423 + 4.5 Combine like terms: 5.196152423 + 4.5 = 9.696152423 x = 9.696152423 Simplifying x = 9.696152423Subproblem 2
x + -4.5 = -5.196152423 Simplifying x + -4.5 = -5.196152423 Reorder the terms: -4.5 + x = -5.196152423 Solving -4.5 + x = -5.196152423 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 = -5.196152423 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.196152423 + 4.5 x = -5.196152423 + 4.5 Combine like terms: -5.196152423 + 4.5 = -0.696152423 x = -0.696152423 Simplifying x = -0.696152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.696152423, -0.696152423}
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