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Simplifying 2x2 + -27x + -8.3 = 0 Reorder the terms: -8.3 + -27x + 2x2 = 0 Solving -8.3 + -27x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.15 + -13.5x + x2 = 0 Move the constant term to the right: Add '4.15' to each side of the equation. -4.15 + -13.5x + 4.15 + x2 = 0 + 4.15 Reorder the terms: -4.15 + 4.15 + -13.5x + x2 = 0 + 4.15 Combine like terms: -4.15 + 4.15 = 0.00 0.00 + -13.5x + x2 = 0 + 4.15 -13.5x + x2 = 0 + 4.15 Combine like terms: 0 + 4.15 = 4.15 -13.5x + x2 = 4.15 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = 4.15 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = 4.15 + 45.5625 Combine like terms: 4.15 + 45.5625 = 49.7125 45.5625 + -13.5x + x2 = 49.7125 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 49.7125 Calculate the square root of the right side: 7.050709184 Break this problem into two subproblems by setting (x + -6.75) equal to 7.050709184 and -7.050709184.Subproblem 1
x + -6.75 = 7.050709184 Simplifying x + -6.75 = 7.050709184 Reorder the terms: -6.75 + x = 7.050709184 Solving -6.75 + x = 7.050709184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 7.050709184 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 7.050709184 + 6.75 x = 7.050709184 + 6.75 Combine like terms: 7.050709184 + 6.75 = 13.800709184 x = 13.800709184 Simplifying x = 13.800709184Subproblem 2
x + -6.75 = -7.050709184 Simplifying x + -6.75 = -7.050709184 Reorder the terms: -6.75 + x = -7.050709184 Solving -6.75 + x = -7.050709184 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -7.050709184 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -7.050709184 + 6.75 x = -7.050709184 + 6.75 Combine like terms: -7.050709184 + 6.75 = -0.300709184 x = -0.300709184 Simplifying x = -0.300709184Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.800709184, -0.300709184}
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