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Simplifying 2x2 + -2x = 49 Reorder the terms: -2x + 2x2 = 49 Solving -2x + 2x2 = 49 Solving for variable 'x'. Reorder the terms: -49 + -2x + 2x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24.5 + -1x + x2 = 0 Move the constant term to the right: Add '24.5' to each side of the equation. -24.5 + -1x + 24.5 + x2 = 0 + 24.5 Reorder the terms: -24.5 + 24.5 + -1x + x2 = 0 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + -1x + x2 = 0 + 24.5 -1x + x2 = 0 + 24.5 Combine like terms: 0 + 24.5 = 24.5 -1x + x2 = 24.5 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 = 24.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 24.5 + 0.25 Combine like terms: 24.5 + 0.25 = 24.75 0.25 + -1x + x2 = 24.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 24.75 Calculate the square root of the right side: 4.974937186 Break this problem into two subproblems by setting (x + -0.5) equal to 4.974937186 and -4.974937186.Subproblem 1
x + -0.5 = 4.974937186 Simplifying x + -0.5 = 4.974937186 Reorder the terms: -0.5 + x = 4.974937186 Solving -0.5 + x = 4.974937186 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 = 4.974937186 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.974937186 + 0.5 x = 4.974937186 + 0.5 Combine like terms: 4.974937186 + 0.5 = 5.474937186 x = 5.474937186 Simplifying x = 5.474937186Subproblem 2
x + -0.5 = -4.974937186 Simplifying x + -0.5 = -4.974937186 Reorder the terms: -0.5 + x = -4.974937186 Solving -0.5 + x = -4.974937186 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 = -4.974937186 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.974937186 + 0.5 x = -4.974937186 + 0.5 Combine like terms: -4.974937186 + 0.5 = -4.474937186 x = -4.474937186 Simplifying x = -4.474937186Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.474937186, -4.474937186}
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