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Simplifying 25x2 + -85x + 56 = 0 Reorder the terms: 56 + -85x + 25x2 = 0 Solving 56 + -85x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 2.24 + -3.4x + x2 = 0 Move the constant term to the right: Add '-2.24' to each side of the equation. 2.24 + -3.4x + -2.24 + x2 = 0 + -2.24 Reorder the terms: 2.24 + -2.24 + -3.4x + x2 = 0 + -2.24 Combine like terms: 2.24 + -2.24 = 0.00 0.00 + -3.4x + x2 = 0 + -2.24 -3.4x + x2 = 0 + -2.24 Combine like terms: 0 + -2.24 = -2.24 -3.4x + x2 = -2.24 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = -2.24 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = -2.24 + 2.89 Combine like terms: -2.24 + 2.89 = 0.65 2.89 + -3.4x + x2 = 0.65 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 0.65 Calculate the square root of the right side: 0.806225775 Break this problem into two subproblems by setting (x + -1.7) equal to 0.806225775 and -0.806225775.Subproblem 1
x + -1.7 = 0.806225775 Simplifying x + -1.7 = 0.806225775 Reorder the terms: -1.7 + x = 0.806225775 Solving -1.7 + x = 0.806225775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 0.806225775 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 0.806225775 + 1.7 x = 0.806225775 + 1.7 Combine like terms: 0.806225775 + 1.7 = 2.506225775 x = 2.506225775 Simplifying x = 2.506225775Subproblem 2
x + -1.7 = -0.806225775 Simplifying x + -1.7 = -0.806225775 Reorder the terms: -1.7 + x = -0.806225775 Solving -1.7 + x = -0.806225775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -0.806225775 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -0.806225775 + 1.7 x = -0.806225775 + 1.7 Combine like terms: -0.806225775 + 1.7 = 0.893774225 x = 0.893774225 Simplifying x = 0.893774225Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.506225775, 0.893774225}
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