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Simplifying 2x2 + -2x + -101 = 0 Reorder the terms: -101 + -2x + 2x2 = 0 Solving -101 + -2x + 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'. -50.5 + -1x + x2 = 0 Move the constant term to the right: Add '50.5' to each side of the equation. -50.5 + -1x + 50.5 + x2 = 0 + 50.5 Reorder the terms: -50.5 + 50.5 + -1x + x2 = 0 + 50.5 Combine like terms: -50.5 + 50.5 = 0.0 0.0 + -1x + x2 = 0 + 50.5 -1x + x2 = 0 + 50.5 Combine like terms: 0 + 50.5 = 50.5 -1x + x2 = 50.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 50.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 50.5 + 0.25 Combine like terms: 50.5 + 0.25 = 50.75 0.25 + -1x + x2 = 50.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 50.75 Calculate the square root of the right side: 7.123903424 Break this problem into two subproblems by setting (x + -0.5) equal to 7.123903424 and -7.123903424.Subproblem 1
x + -0.5 = 7.123903424 Simplifying x + -0.5 = 7.123903424 Reorder the terms: -0.5 + x = 7.123903424 Solving -0.5 + x = 7.123903424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 7.123903424 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 7.123903424 + 0.5 x = 7.123903424 + 0.5 Combine like terms: 7.123903424 + 0.5 = 7.623903424 x = 7.623903424 Simplifying x = 7.623903424Subproblem 2
x + -0.5 = -7.123903424 Simplifying x + -0.5 = -7.123903424 Reorder the terms: -0.5 + x = -7.123903424 Solving -0.5 + x = -7.123903424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -7.123903424 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -7.123903424 + 0.5 x = -7.123903424 + 0.5 Combine like terms: -7.123903424 + 0.5 = -6.623903424 x = -6.623903424 Simplifying x = -6.623903424Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.623903424, -6.623903424}
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