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Simplifying 25x2 + 100x + 81 = 0 Reorder the terms: 81 + 100x + 25x2 = 0 Solving 81 + 100x + 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'. 3.24 + 4x + x2 = 0 Move the constant term to the right: Add '-3.24' to each side of the equation. 3.24 + 4x + -3.24 + x2 = 0 + -3.24 Reorder the terms: 3.24 + -3.24 + 4x + x2 = 0 + -3.24 Combine like terms: 3.24 + -3.24 = 0.00 0.00 + 4x + x2 = 0 + -3.24 4x + x2 = 0 + -3.24 Combine like terms: 0 + -3.24 = -3.24 4x + x2 = -3.24 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -3.24 + 4 Reorder the terms: 4 + 4x + x2 = -3.24 + 4 Combine like terms: -3.24 + 4 = 0.76 4 + 4x + x2 = 0.76 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (x + 2) equal to 0.871779789 and -0.871779789.Subproblem 1
x + 2 = 0.871779789 Simplifying x + 2 = 0.871779789 Reorder the terms: 2 + x = 0.871779789 Solving 2 + x = 0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0.871779789 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.871779789 + -2 x = 0.871779789 + -2 Combine like terms: 0.871779789 + -2 = -1.128220211 x = -1.128220211 Simplifying x = -1.128220211Subproblem 2
x + 2 = -0.871779789 Simplifying x + 2 = -0.871779789 Reorder the terms: 2 + x = -0.871779789 Solving 2 + x = -0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -0.871779789 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.871779789 + -2 x = -0.871779789 + -2 Combine like terms: -0.871779789 + -2 = -2.871779789 x = -2.871779789 Simplifying x = -2.871779789Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.128220211, -2.871779789}
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