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Simplifying 2x2 + (6x + -9x) + (2 + -8) = 0 Combine like terms: 6x + -9x = -3x 2x2 + (-3x) + (2 + -8) = 0 2x2 + (-3x) + (2 + -8) = 0 Combine like terms: 2 + -8 = -6 2x2 + (-3x) + (-6) = 0 2x2 + (-3x) + -6 = 0 Reorder the terms: -6 + (-3x) + 2x2 = 0 Solving -6 + (-3x) + 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'. -3 + (-1.5x) + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + (-1.5x) + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + (-1.5x) + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + (-1.5x) + x2 = 0 + 3 (-1.5x) + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 (-1.5x) + x2 = 3 The x term is (-1.5x). Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. (-1.5x) + 0.5625 + x2 = 3 + 0.5625 Reorder the terms: 0.5625 + (-1.5x) + x2 = 3 + 0.5625 Combine like terms: 3 + 0.5625 = 3.5625 0.5625 + (-1.5x) + x2 = 3.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + -0.75) equal to 1.887458609 and -1.887458609.Subproblem 1
x + -0.75 = 1.887458609 Simplifying x + -0.75 = 1.887458609 Reorder the terms: -0.75 + x = 1.887458609 Solving -0.75 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.887458609 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.887458609 + 0.75 x = 1.887458609 + 0.75 Combine like terms: 1.887458609 + 0.75 = 2.637458609 x = 2.637458609 Simplifying x = 2.637458609Subproblem 2
x + -0.75 = -1.887458609 Simplifying x + -0.75 = -1.887458609 Reorder the terms: -0.75 + x = -1.887458609 Solving -0.75 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.887458609 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.887458609 + 0.75 x = -1.887458609 + 0.75 Combine like terms: -1.887458609 + 0.75 = -1.137458609 x = -1.137458609 Simplifying x = -1.137458609Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.637458609, -1.137458609}
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