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Simplifying 25x2 + -40x = -11 Reorder the terms: -40x + 25x2 = -11 Solving -40x + 25x2 = -11 Solving for variable 'x'. Reorder the terms: 11 + -40x + 25x2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + -40x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.44 + -1.6x + x2 = 0 Move the constant term to the right: Add '-0.44' to each side of the equation. 0.44 + -1.6x + -0.44 + x2 = 0 + -0.44 Reorder the terms: 0.44 + -0.44 + -1.6x + x2 = 0 + -0.44 Combine like terms: 0.44 + -0.44 = 0.00 0.00 + -1.6x + x2 = 0 + -0.44 -1.6x + x2 = 0 + -0.44 Combine like terms: 0 + -0.44 = -0.44 -1.6x + x2 = -0.44 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 = -0.44 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = -0.44 + 0.64 Combine like terms: -0.44 + 0.64 = 0.2 0.64 + -1.6x + x2 = 0.2 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (x + -0.8) equal to 0.447213596 and -0.447213596.Subproblem 1
x + -0.8 = 0.447213596 Simplifying x + -0.8 = 0.447213596 Reorder the terms: -0.8 + x = 0.447213596 Solving -0.8 + x = 0.447213596 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 = 0.447213596 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 0.447213596 + 0.8 x = 0.447213596 + 0.8 Combine like terms: 0.447213596 + 0.8 = 1.247213596 x = 1.247213596 Simplifying x = 1.247213596Subproblem 2
x + -0.8 = -0.447213596 Simplifying x + -0.8 = -0.447213596 Reorder the terms: -0.8 + x = -0.447213596 Solving -0.8 + x = -0.447213596 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 = -0.447213596 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -0.447213596 + 0.8 x = -0.447213596 + 0.8 Combine like terms: -0.447213596 + 0.8 = 0.352786404 x = 0.352786404 Simplifying x = 0.352786404Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.247213596, 0.352786404}
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