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Simplifying 2x2 + 2x + -10 = 101 Reorder the terms: -10 + 2x + 2x2 = 101 Solving -10 + 2x + 2x2 = 101 Solving for variable 'x'. Reorder the terms: -10 + -101 + 2x + 2x2 = 101 + -101 Combine like terms: -10 + -101 = -111 -111 + 2x + 2x2 = 101 + -101 Combine like terms: 101 + -101 = 0 -111 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -55.5 + x + x2 = 0 Move the constant term to the right: Add '55.5' to each side of the equation. -55.5 + x + 55.5 + x2 = 0 + 55.5 Reorder the terms: -55.5 + 55.5 + x + x2 = 0 + 55.5 Combine like terms: -55.5 + 55.5 = 0.0 0.0 + x + x2 = 0 + 55.5 x + x2 = 0 + 55.5 Combine like terms: 0 + 55.5 = 55.5 x + x2 = 55.5 The x term is x. 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. + 0.25 + x2 = 55.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 55.5 + 0.25 Combine like terms: 55.5 + 0.25 = 55.75 1.25 + x2 = 55.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 55.75 Calculate the square root of the right side: 7.466592262 Break this problem into two subproblems by setting (x + 0.5) equal to 7.466592262 and -7.466592262.Subproblem 1
x + 0.5 = 7.466592262 Simplifying x + 0.5 = 7.466592262 Reorder the terms: 0.5 + x = 7.466592262 Solving 0.5 + x = 7.466592262 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 = 7.466592262 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.466592262 + -0.5 x = 7.466592262 + -0.5 Combine like terms: 7.466592262 + -0.5 = 6.966592262 x = 6.966592262 Simplifying x = 6.966592262Subproblem 2
x + 0.5 = -7.466592262 Simplifying x + 0.5 = -7.466592262 Reorder the terms: 0.5 + x = -7.466592262 Solving 0.5 + x = -7.466592262 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 = -7.466592262 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.466592262 + -0.5 x = -7.466592262 + -0.5 Combine like terms: -7.466592262 + -0.5 = -7.966592262 x = -7.966592262 Simplifying x = -7.966592262Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.966592262, -7.966592262}
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