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Simplifying 2x2 + 10x + 25 = 110 Reorder the terms: 25 + 10x + 2x2 = 110 Solving 25 + 10x + 2x2 = 110 Solving for variable 'x'. Reorder the terms: 25 + -110 + 10x + 2x2 = 110 + -110 Combine like terms: 25 + -110 = -85 -85 + 10x + 2x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -85 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -42.5 + 5x + x2 = 0 Move the constant term to the right: Add '42.5' to each side of the equation. -42.5 + 5x + 42.5 + x2 = 0 + 42.5 Reorder the terms: -42.5 + 42.5 + 5x + x2 = 0 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + 5x + x2 = 0 + 42.5 5x + x2 = 0 + 42.5 Combine like terms: 0 + 42.5 = 42.5 5x + x2 = 42.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 42.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 42.5 + 6.25 Combine like terms: 42.5 + 6.25 = 48.75 6.25 + 5x + x2 = 48.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 48.75 Calculate the square root of the right side: 6.982120022 Break this problem into two subproblems by setting (x + 2.5) equal to 6.982120022 and -6.982120022.Subproblem 1
x + 2.5 = 6.982120022 Simplifying x + 2.5 = 6.982120022 Reorder the terms: 2.5 + x = 6.982120022 Solving 2.5 + x = 6.982120022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 6.982120022 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 6.982120022 + -2.5 x = 6.982120022 + -2.5 Combine like terms: 6.982120022 + -2.5 = 4.482120022 x = 4.482120022 Simplifying x = 4.482120022Subproblem 2
x + 2.5 = -6.982120022 Simplifying x + 2.5 = -6.982120022 Reorder the terms: 2.5 + x = -6.982120022 Solving 2.5 + x = -6.982120022 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -6.982120022 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -6.982120022 + -2.5 x = -6.982120022 + -2.5 Combine like terms: -6.982120022 + -2.5 = -9.482120022 x = -9.482120022 Simplifying x = -9.482120022Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.482120022, -9.482120022}
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