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Simplifying 4x2 + -25x + 20 = 0 Reorder the terms: 20 + -25x + 4x2 = 0 Solving 20 + -25x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5 + -6.25x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -6.25x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -6.25x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6.25x + x2 = 0 + -5 -6.25x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -6.25x + x2 = -5 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = -5 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = -5 + 9.765625 Combine like terms: -5 + 9.765625 = 4.765625 9.765625 + -6.25x + x2 = 4.765625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 4.765625 Calculate the square root of the right side: 2.18303115 Break this problem into two subproblems by setting (x + -3.125) equal to 2.18303115 and -2.18303115.Subproblem 1
x + -3.125 = 2.18303115 Simplifying x + -3.125 = 2.18303115 Reorder the terms: -3.125 + x = 2.18303115 Solving -3.125 + x = 2.18303115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 2.18303115 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 2.18303115 + 3.125 x = 2.18303115 + 3.125 Combine like terms: 2.18303115 + 3.125 = 5.30803115 x = 5.30803115 Simplifying x = 5.30803115Subproblem 2
x + -3.125 = -2.18303115 Simplifying x + -3.125 = -2.18303115 Reorder the terms: -3.125 + x = -2.18303115 Solving -3.125 + x = -2.18303115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -2.18303115 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -2.18303115 + 3.125 x = -2.18303115 + 3.125 Combine like terms: -2.18303115 + 3.125 = 0.94196885 x = 0.94196885 Simplifying x = 0.94196885Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.30803115, 0.94196885}
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