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Simplifying -4x2 + -10x + 25 = 0 Reorder the terms: 25 + -10x + -4x2 = 0 Solving 25 + -10x + -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'. -6.25 + 2.5x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 2.5x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 2.5x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 2.5x + x2 = 0 + 6.25 2.5x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 2.5x + x2 = 6.25 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 6.25 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 6.25 + 1.5625 Combine like terms: 6.25 + 1.5625 = 7.8125 1.5625 + 2.5x + x2 = 7.8125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 7.8125 Calculate the square root of the right side: 2.795084972 Break this problem into two subproblems by setting (x + 1.25) equal to 2.795084972 and -2.795084972.Subproblem 1
x + 1.25 = 2.795084972 Simplifying x + 1.25 = 2.795084972 Reorder the terms: 1.25 + x = 2.795084972 Solving 1.25 + x = 2.795084972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.795084972 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.795084972 + -1.25 x = 2.795084972 + -1.25 Combine like terms: 2.795084972 + -1.25 = 1.545084972 x = 1.545084972 Simplifying x = 1.545084972Subproblem 2
x + 1.25 = -2.795084972 Simplifying x + 1.25 = -2.795084972 Reorder the terms: 1.25 + x = -2.795084972 Solving 1.25 + x = -2.795084972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.795084972 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.795084972 + -1.25 x = -2.795084972 + -1.25 Combine like terms: -2.795084972 + -1.25 = -4.045084972 x = -4.045084972 Simplifying x = -4.045084972Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.545084972, -4.045084972}
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