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Simplifying 25x2 + -40x + -18 = 0 Reorder the terms: -18 + -40x + 25x2 = 0 Solving -18 + -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'. -0.72 + -1.6x + x2 = 0 Move the constant term to the right: Add '0.72' to each side of the equation. -0.72 + -1.6x + 0.72 + x2 = 0 + 0.72 Reorder the terms: -0.72 + 0.72 + -1.6x + x2 = 0 + 0.72 Combine like terms: -0.72 + 0.72 = 0.00 0.00 + -1.6x + x2 = 0 + 0.72 -1.6x + x2 = 0 + 0.72 Combine like terms: 0 + 0.72 = 0.72 -1.6x + x2 = 0.72 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 = 0.72 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 0.72 + 0.64 Combine like terms: 0.72 + 0.64 = 1.36 0.64 + -1.6x + x2 = 1.36 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 1.36 Calculate the square root of the right side: 1.166190379 Break this problem into two subproblems by setting (x + -0.8) equal to 1.166190379 and -1.166190379.Subproblem 1
x + -0.8 = 1.166190379 Simplifying x + -0.8 = 1.166190379 Reorder the terms: -0.8 + x = 1.166190379 Solving -0.8 + x = 1.166190379 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 = 1.166190379 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.166190379 + 0.8 x = 1.166190379 + 0.8 Combine like terms: 1.166190379 + 0.8 = 1.966190379 x = 1.966190379 Simplifying x = 1.966190379Subproblem 2
x + -0.8 = -1.166190379 Simplifying x + -0.8 = -1.166190379 Reorder the terms: -0.8 + x = -1.166190379 Solving -0.8 + x = -1.166190379 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 = -1.166190379 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.166190379 + 0.8 x = -1.166190379 + 0.8 Combine like terms: -1.166190379 + 0.8 = -0.366190379 x = -0.366190379 Simplifying x = -0.366190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.966190379, -0.366190379}
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