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Simplifying 2x2 + 6x + -135 = 0 Reorder the terms: -135 + 6x + 2x2 = 0 Solving -135 + 6x + 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'. -67.5 + 3x + x2 = 0 Move the constant term to the right: Add '67.5' to each side of the equation. -67.5 + 3x + 67.5 + x2 = 0 + 67.5 Reorder the terms: -67.5 + 67.5 + 3x + x2 = 0 + 67.5 Combine like terms: -67.5 + 67.5 = 0.0 0.0 + 3x + x2 = 0 + 67.5 3x + x2 = 0 + 67.5 Combine like terms: 0 + 67.5 = 67.5 3x + x2 = 67.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 67.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 67.5 + 2.25 Combine like terms: 67.5 + 2.25 = 69.75 2.25 + 3x + x2 = 69.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 69.75 Calculate the square root of the right side: 8.351646544 Break this problem into two subproblems by setting (x + 1.5) equal to 8.351646544 and -8.351646544.Subproblem 1
x + 1.5 = 8.351646544 Simplifying x + 1.5 = 8.351646544 Reorder the terms: 1.5 + x = 8.351646544 Solving 1.5 + x = 8.351646544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 8.351646544 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 8.351646544 + -1.5 x = 8.351646544 + -1.5 Combine like terms: 8.351646544 + -1.5 = 6.851646544 x = 6.851646544 Simplifying x = 6.851646544Subproblem 2
x + 1.5 = -8.351646544 Simplifying x + 1.5 = -8.351646544 Reorder the terms: 1.5 + x = -8.351646544 Solving 1.5 + x = -8.351646544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -8.351646544 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -8.351646544 + -1.5 x = -8.351646544 + -1.5 Combine like terms: -8.351646544 + -1.5 = -9.851646544 x = -9.851646544 Simplifying x = -9.851646544Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.851646544, -9.851646544}
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