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Simplifying 2x2 + -2x = 44.5 Reorder the terms: -2x + 2x2 = 44.5 Solving -2x + 2x2 = 44.5 Solving for variable 'x'. Reorder the terms: -44.5 + -2x + 2x2 = 44.5 + -44.5 Combine like terms: 44.5 + -44.5 = 0.0 -44.5 + -2x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.25 + -1x + x2 = 0.0 Move the constant term to the right: Add '22.25' to each side of the equation. -22.25 + -1x + 22.25 + x2 = 0.0 + 22.25 Reorder the terms: -22.25 + 22.25 + -1x + x2 = 0.0 + 22.25 Combine like terms: -22.25 + 22.25 = 0.00 0.00 + -1x + x2 = 0.0 + 22.25 -1x + x2 = 0.0 + 22.25 Combine like terms: 0.0 + 22.25 = 22.25 -1x + x2 = 22.25 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 = 22.25 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 22.25 + 0.25 Combine like terms: 22.25 + 0.25 = 22.5 0.25 + -1x + x2 = 22.5 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 22.5 Calculate the square root of the right side: 4.74341649 Break this problem into two subproblems by setting (x + -0.5) equal to 4.74341649 and -4.74341649.Subproblem 1
x + -0.5 = 4.74341649 Simplifying x + -0.5 = 4.74341649 Reorder the terms: -0.5 + x = 4.74341649 Solving -0.5 + x = 4.74341649 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 = 4.74341649 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 4.74341649 + 0.5 x = 4.74341649 + 0.5 Combine like terms: 4.74341649 + 0.5 = 5.24341649 x = 5.24341649 Simplifying x = 5.24341649Subproblem 2
x + -0.5 = -4.74341649 Simplifying x + -0.5 = -4.74341649 Reorder the terms: -0.5 + x = -4.74341649 Solving -0.5 + x = -4.74341649 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 = -4.74341649 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -4.74341649 + 0.5 x = -4.74341649 + 0.5 Combine like terms: -4.74341649 + 0.5 = -4.24341649 x = -4.24341649 Simplifying x = -4.24341649Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.24341649, -4.24341649}
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