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Simplifying 25x2 + -1x + -8 = 0 Reorder the terms: -8 + -1x + 25x2 = 0 Solving -8 + -1x + 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 + -0.04x + x2 = 0 Move the constant term to the right: Add '0.32' to each side of the equation. -0.32 + -0.04x + 0.32 + x2 = 0 + 0.32 Reorder the terms: -0.32 + 0.32 + -0.04x + x2 = 0 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + -0.04x + x2 = 0 + 0.32 -0.04x + x2 = 0 + 0.32 Combine like terms: 0 + 0.32 = 0.32 -0.04x + x2 = 0.32 The x term is -0.04x. Take half its coefficient (-0.02). Square it (0.0004) and add it to both sides. Add '0.0004' to each side of the equation. -0.04x + 0.0004 + x2 = 0.32 + 0.0004 Reorder the terms: 0.0004 + -0.04x + x2 = 0.32 + 0.0004 Combine like terms: 0.32 + 0.0004 = 0.3204 0.0004 + -0.04x + x2 = 0.3204 Factor a perfect square on the left side: (x + -0.02)(x + -0.02) = 0.3204 Calculate the square root of the right side: 0.566038868 Break this problem into two subproblems by setting (x + -0.02) equal to 0.566038868 and -0.566038868.Subproblem 1
x + -0.02 = 0.566038868 Simplifying x + -0.02 = 0.566038868 Reorder the terms: -0.02 + x = 0.566038868 Solving -0.02 + x = 0.566038868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + x = 0.566038868 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = 0.566038868 + 0.02 x = 0.566038868 + 0.02 Combine like terms: 0.566038868 + 0.02 = 0.586038868 x = 0.586038868 Simplifying x = 0.586038868Subproblem 2
x + -0.02 = -0.566038868 Simplifying x + -0.02 = -0.566038868 Reorder the terms: -0.02 + x = -0.566038868 Solving -0.02 + x = -0.566038868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02' to each side of the equation. -0.02 + 0.02 + x = -0.566038868 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + x = -0.566038868 + 0.02 x = -0.566038868 + 0.02 Combine like terms: -0.566038868 + 0.02 = -0.546038868 x = -0.546038868 Simplifying x = -0.546038868Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.586038868, -0.546038868}
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