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Simplifying 2.2x2 + 6x + -95 = 0 Reorder the terms: -95 + 6x + 2.2x2 = 0 Solving -95 + 6x + 2.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.2 the coefficient of the squared term: Divide each side by '2.2'. -43.18181818 + 2.727272727x + x2 = 0 Move the constant term to the right: Add '43.18181818' to each side of the equation. -43.18181818 + 2.727272727x + 43.18181818 + x2 = 0 + 43.18181818 Reorder the terms: -43.18181818 + 43.18181818 + 2.727272727x + x2 = 0 + 43.18181818 Combine like terms: -43.18181818 + 43.18181818 = 0.00000000 0.00000000 + 2.727272727x + x2 = 0 + 43.18181818 2.727272727x + x2 = 0 + 43.18181818 Combine like terms: 0 + 43.18181818 = 43.18181818 2.727272727x + x2 = 43.18181818 The x term is 2.727272727x. Take half its coefficient (1.363636364). Square it (1.859504133) and add it to both sides. Add '1.859504133' to each side of the equation. 2.727272727x + 1.859504133 + x2 = 43.18181818 + 1.859504133 Reorder the terms: 1.859504133 + 2.727272727x + x2 = 43.18181818 + 1.859504133 Combine like terms: 43.18181818 + 1.859504133 = 45.041322313 1.859504133 + 2.727272727x + x2 = 45.041322313 Factor a perfect square on the left side: (x + 1.363636364)(x + 1.363636364) = 45.041322313 Calculate the square root of the right side: 6.711283209 Break this problem into two subproblems by setting (x + 1.363636364) equal to 6.711283209 and -6.711283209.Subproblem 1
x + 1.363636364 = 6.711283209 Simplifying x + 1.363636364 = 6.711283209 Reorder the terms: 1.363636364 + x = 6.711283209 Solving 1.363636364 + x = 6.711283209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.363636364' to each side of the equation. 1.363636364 + -1.363636364 + x = 6.711283209 + -1.363636364 Combine like terms: 1.363636364 + -1.363636364 = 0.000000000 0.000000000 + x = 6.711283209 + -1.363636364 x = 6.711283209 + -1.363636364 Combine like terms: 6.711283209 + -1.363636364 = 5.347646845 x = 5.347646845 Simplifying x = 5.347646845Subproblem 2
x + 1.363636364 = -6.711283209 Simplifying x + 1.363636364 = -6.711283209 Reorder the terms: 1.363636364 + x = -6.711283209 Solving 1.363636364 + x = -6.711283209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.363636364' to each side of the equation. 1.363636364 + -1.363636364 + x = -6.711283209 + -1.363636364 Combine like terms: 1.363636364 + -1.363636364 = 0.000000000 0.000000000 + x = -6.711283209 + -1.363636364 x = -6.711283209 + -1.363636364 Combine like terms: -6.711283209 + -1.363636364 = -8.074919573 x = -8.074919573 Simplifying x = -8.074919573Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.347646845, -8.074919573}
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