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Simplifying 25x2 + -40x + 8 = 0 Reorder the terms: 8 + -40x + 25x2 = 0 Solving 8 + -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'. 0.32 + -1.6x + x2 = 0 Move the constant term to the right: Add '-0.32' to each side of the equation. 0.32 + -1.6x + -0.32 + x2 = 0 + -0.32 Reorder the terms: 0.32 + -0.32 + -1.6x + x2 = 0 + -0.32 Combine like terms: 0.32 + -0.32 = 0.00 0.00 + -1.6x + x2 = 0 + -0.32 -1.6x + x2 = 0 + -0.32 Combine like terms: 0 + -0.32 = -0.32 -1.6x + x2 = -0.32 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 = -0.32 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = -0.32 + 0.64 Combine like terms: -0.32 + 0.64 = 0.32 0.64 + -1.6x + x2 = 0.32 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 0.32 Calculate the square root of the right side: 0.565685425 Break this problem into two subproblems by setting (x + -0.8) equal to 0.565685425 and -0.565685425.Subproblem 1
x + -0.8 = 0.565685425 Simplifying x + -0.8 = 0.565685425 Reorder the terms: -0.8 + x = 0.565685425 Solving -0.8 + x = 0.565685425 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 = 0.565685425 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 0.565685425 + 0.8 x = 0.565685425 + 0.8 Combine like terms: 0.565685425 + 0.8 = 1.365685425 x = 1.365685425 Simplifying x = 1.365685425Subproblem 2
x + -0.8 = -0.565685425 Simplifying x + -0.8 = -0.565685425 Reorder the terms: -0.8 + x = -0.565685425 Solving -0.8 + x = -0.565685425 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 = -0.565685425 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -0.565685425 + 0.8 x = -0.565685425 + 0.8 Combine like terms: -0.565685425 + 0.8 = 0.234314575 x = 0.234314575 Simplifying x = 0.234314575Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.365685425, 0.234314575}
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