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Simplifying 25x2 + -40x = 31 Reorder the terms: -40x + 25x2 = 31 Solving -40x + 25x2 = 31 Solving for variable 'x'. Reorder the terms: -31 + -40x + 25x2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + -40x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1.24 + -1.6x + x2 = 0 Move the constant term to the right: Add '1.24' to each side of the equation. -1.24 + -1.6x + 1.24 + x2 = 0 + 1.24 Reorder the terms: -1.24 + 1.24 + -1.6x + x2 = 0 + 1.24 Combine like terms: -1.24 + 1.24 = 0.00 0.00 + -1.6x + x2 = 0 + 1.24 -1.6x + x2 = 0 + 1.24 Combine like terms: 0 + 1.24 = 1.24 -1.6x + x2 = 1.24 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 = 1.24 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 1.24 + 0.64 Combine like terms: 1.24 + 0.64 = 1.88 0.64 + -1.6x + x2 = 1.88 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 1.88 Calculate the square root of the right side: 1.37113092 Break this problem into two subproblems by setting (x + -0.8) equal to 1.37113092 and -1.37113092.Subproblem 1
x + -0.8 = 1.37113092 Simplifying x + -0.8 = 1.37113092 Reorder the terms: -0.8 + x = 1.37113092 Solving -0.8 + x = 1.37113092 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 = 1.37113092 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.37113092 + 0.8 x = 1.37113092 + 0.8 Combine like terms: 1.37113092 + 0.8 = 2.17113092 x = 2.17113092 Simplifying x = 2.17113092Subproblem 2
x + -0.8 = -1.37113092 Simplifying x + -0.8 = -1.37113092 Reorder the terms: -0.8 + x = -1.37113092 Solving -0.8 + x = -1.37113092 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 = -1.37113092 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.37113092 + 0.8 x = -1.37113092 + 0.8 Combine like terms: -1.37113092 + 0.8 = -0.57113092 x = -0.57113092 Simplifying x = -0.57113092Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.17113092, -0.57113092}
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