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Simplifying 4x2 + 50x + 125 = 0 Reorder the terms: 125 + 50x + 4x2 = 0 Solving 125 + 50x + 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'. 31.25 + 12.5x + x2 = 0 Move the constant term to the right: Add '-31.25' to each side of the equation. 31.25 + 12.5x + -31.25 + x2 = 0 + -31.25 Reorder the terms: 31.25 + -31.25 + 12.5x + x2 = 0 + -31.25 Combine like terms: 31.25 + -31.25 = 0.00 0.00 + 12.5x + x2 = 0 + -31.25 12.5x + x2 = 0 + -31.25 Combine like terms: 0 + -31.25 = -31.25 12.5x + x2 = -31.25 The x term is 12.5x. Take half its coefficient (6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. 12.5x + 39.0625 + x2 = -31.25 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = -31.25 + 39.0625 Combine like terms: -31.25 + 39.0625 = 7.8125 39.0625 + 12.5x + x2 = 7.8125 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 7.8125 Calculate the square root of the right side: 2.795084972 Break this problem into two subproblems by setting (x + 6.25) equal to 2.795084972 and -2.795084972.Subproblem 1
x + 6.25 = 2.795084972 Simplifying x + 6.25 = 2.795084972 Reorder the terms: 6.25 + x = 2.795084972 Solving 6.25 + x = 2.795084972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 2.795084972 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 2.795084972 + -6.25 x = 2.795084972 + -6.25 Combine like terms: 2.795084972 + -6.25 = -3.454915028 x = -3.454915028 Simplifying x = -3.454915028Subproblem 2
x + 6.25 = -2.795084972 Simplifying x + 6.25 = -2.795084972 Reorder the terms: 6.25 + x = -2.795084972 Solving 6.25 + x = -2.795084972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -2.795084972 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -2.795084972 + -6.25 x = -2.795084972 + -6.25 Combine like terms: -2.795084972 + -6.25 = -9.045084972 x = -9.045084972 Simplifying x = -9.045084972Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.454915028, -9.045084972}
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