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Simplifying -11x2 + 6x + 195 = 0 Reorder the terms: 195 + 6x + -11x2 = 0 Solving 195 + 6x + -11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -17.72727273 + -0.5454545455x + x2 = 0 Move the constant term to the right: Add '17.72727273' to each side of the equation. -17.72727273 + -0.5454545455x + 17.72727273 + x2 = 0 + 17.72727273 Reorder the terms: -17.72727273 + 17.72727273 + -0.5454545455x + x2 = 0 + 17.72727273 Combine like terms: -17.72727273 + 17.72727273 = 0.00000000 0.00000000 + -0.5454545455x + x2 = 0 + 17.72727273 -0.5454545455x + x2 = 0 + 17.72727273 Combine like terms: 0 + 17.72727273 = 17.72727273 -0.5454545455x + x2 = 17.72727273 The x term is -0.5454545455x. Take half its coefficient (-0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. -0.5454545455x + 0.07438016533 + x2 = 17.72727273 + 0.07438016533 Reorder the terms: 0.07438016533 + -0.5454545455x + x2 = 17.72727273 + 0.07438016533 Combine like terms: 17.72727273 + 0.07438016533 = 17.80165289533 0.07438016533 + -0.5454545455x + x2 = 17.80165289533 Factor a perfect square on the left side: (x + -0.2727272728)(x + -0.2727272728) = 17.80165289533 Calculate the square root of the right side: 4.219200504 Break this problem into two subproblems by setting (x + -0.2727272728) equal to 4.219200504 and -4.219200504.Subproblem 1
x + -0.2727272728 = 4.219200504 Simplifying x + -0.2727272728 = 4.219200504 Reorder the terms: -0.2727272728 + x = 4.219200504 Solving -0.2727272728 + x = 4.219200504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = 4.219200504 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = 4.219200504 + 0.2727272728 x = 4.219200504 + 0.2727272728 Combine like terms: 4.219200504 + 0.2727272728 = 4.4919277768 x = 4.4919277768 Simplifying x = 4.4919277768Subproblem 2
x + -0.2727272728 = -4.219200504 Simplifying x + -0.2727272728 = -4.219200504 Reorder the terms: -0.2727272728 + x = -4.219200504 Solving -0.2727272728 + x = -4.219200504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = -4.219200504 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = -4.219200504 + 0.2727272728 x = -4.219200504 + 0.2727272728 Combine like terms: -4.219200504 + 0.2727272728 = -3.9464732312 x = -3.9464732312 Simplifying x = -3.9464732312Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.4919277768, -3.9464732312}
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