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Simplifying 25x2 + -40x + -34 = 0 Reorder the terms: -34 + -40x + 25x2 = 0 Solving -34 + -40x + 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'. -1.36 + -1.6x + x2 = 0 Move the constant term to the right: Add '1.36' to each side of the equation. -1.36 + -1.6x + 1.36 + x2 = 0 + 1.36 Reorder the terms: -1.36 + 1.36 + -1.6x + x2 = 0 + 1.36 Combine like terms: -1.36 + 1.36 = 0.00 0.00 + -1.6x + x2 = 0 + 1.36 -1.6x + x2 = 0 + 1.36 Combine like terms: 0 + 1.36 = 1.36 -1.6x + x2 = 1.36 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 1.36 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 1.36 + 0.64 Combine like terms: 1.36 + 0.64 = 2 0.64 + -1.6x + x2 = 2 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -0.8) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -0.8 = 1.414213562 Simplifying x + -0.8 = 1.414213562 Reorder the terms: -0.8 + x = 1.414213562 Solving -0.8 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 1.414213562 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.414213562 + 0.8 x = 1.414213562 + 0.8 Combine like terms: 1.414213562 + 0.8 = 2.214213562 x = 2.214213562 Simplifying x = 2.214213562Subproblem 2
x + -0.8 = -1.414213562 Simplifying x + -0.8 = -1.414213562 Reorder the terms: -0.8 + x = -1.414213562 Solving -0.8 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -1.414213562 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.414213562 + 0.8 x = -1.414213562 + 0.8 Combine like terms: -1.414213562 + 0.8 = -0.614213562 x = -0.614213562 Simplifying x = -0.614213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.214213562, -0.614213562}
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