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Simplifying 25x2 + 110x + -85 = 0 Reorder the terms: -85 + 110x + 25x2 = 0 Solving -85 + 110x + 25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-17 + 22x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-17 + 22x + 5x2)' equal to zero and attempt to solve: Simplifying -17 + 22x + 5x2 = 0 Solving -17 + 22x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.4 + 4.4x + x2 = 0 Move the constant term to the right: Add '3.4' to each side of the equation. -3.4 + 4.4x + 3.4 + x2 = 0 + 3.4 Reorder the terms: -3.4 + 3.4 + 4.4x + x2 = 0 + 3.4 Combine like terms: -3.4 + 3.4 = 0.0 0.0 + 4.4x + x2 = 0 + 3.4 4.4x + x2 = 0 + 3.4 Combine like terms: 0 + 3.4 = 3.4 4.4x + x2 = 3.4 The x term is 4.4x. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4x + 4.84 + x2 = 3.4 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = 3.4 + 4.84 Combine like terms: 3.4 + 4.84 = 8.24 4.84 + 4.4x + x2 = 8.24 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = 8.24 Calculate the square root of the right side: 2.870540019 Break this problem into two subproblems by setting (x + 2.2) equal to 2.870540019 and -2.870540019.Subproblem 1
x + 2.2 = 2.870540019 Simplifying x + 2.2 = 2.870540019 Reorder the terms: 2.2 + x = 2.870540019 Solving 2.2 + x = 2.870540019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = 2.870540019 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 2.870540019 + -2.2 x = 2.870540019 + -2.2 Combine like terms: 2.870540019 + -2.2 = 0.670540019 x = 0.670540019 Simplifying x = 0.670540019Subproblem 2
x + 2.2 = -2.870540019 Simplifying x + 2.2 = -2.870540019 Reorder the terms: 2.2 + x = -2.870540019 Solving 2.2 + x = -2.870540019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = -2.870540019 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -2.870540019 + -2.2 x = -2.870540019 + -2.2 Combine like terms: -2.870540019 + -2.2 = -5.070540019 x = -5.070540019 Simplifying x = -5.070540019Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.670540019, -5.070540019}Solution
x = {0.670540019, -5.070540019}
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