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Simplifying 25x2 + -11x + -25 = 0 Reorder the terms: -25 + -11x + 25x2 = 0 Solving -25 + -11x + 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'. -1 + -0.44x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.44x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.44x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.44x + x2 = 0 + 1 -0.44x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.44x + x2 = 1 The x term is -0.44x. Take half its coefficient (-0.22). Square it (0.0484) and add it to both sides. Add '0.0484' to each side of the equation. -0.44x + 0.0484 + x2 = 1 + 0.0484 Reorder the terms: 0.0484 + -0.44x + x2 = 1 + 0.0484 Combine like terms: 1 + 0.0484 = 1.0484 0.0484 + -0.44x + x2 = 1.0484 Factor a perfect square on the left side: (x + -0.22)(x + -0.22) = 1.0484 Calculate the square root of the right side: 1.023914059 Break this problem into two subproblems by setting (x + -0.22) equal to 1.023914059 and -1.023914059.Subproblem 1
x + -0.22 = 1.023914059 Simplifying x + -0.22 = 1.023914059 Reorder the terms: -0.22 + x = 1.023914059 Solving -0.22 + x = 1.023914059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.22' to each side of the equation. -0.22 + 0.22 + x = 1.023914059 + 0.22 Combine like terms: -0.22 + 0.22 = 0.00 0.00 + x = 1.023914059 + 0.22 x = 1.023914059 + 0.22 Combine like terms: 1.023914059 + 0.22 = 1.243914059 x = 1.243914059 Simplifying x = 1.243914059Subproblem 2
x + -0.22 = -1.023914059 Simplifying x + -0.22 = -1.023914059 Reorder the terms: -0.22 + x = -1.023914059 Solving -0.22 + x = -1.023914059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.22' to each side of the equation. -0.22 + 0.22 + x = -1.023914059 + 0.22 Combine like terms: -0.22 + 0.22 = 0.00 0.00 + x = -1.023914059 + 0.22 x = -1.023914059 + 0.22 Combine like terms: -1.023914059 + 0.22 = -0.803914059 x = -0.803914059 Simplifying x = -0.803914059Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.243914059, -0.803914059}
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