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Simplifying 25x2 + -12x + -1 = 0 Reorder the terms: -1 + -12x + 25x2 = 0 Solving -1 + -12x + 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'. -0.04 + -0.48x + x2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + -0.48x + 0.04 + x2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + -0.48x + x2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + -0.48x + x2 = 0 + 0.04 -0.48x + x2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 -0.48x + x2 = 0.04 The x term is -0.48x. Take half its coefficient (-0.24). Square it (0.0576) and add it to both sides. Add '0.0576' to each side of the equation. -0.48x + 0.0576 + x2 = 0.04 + 0.0576 Reorder the terms: 0.0576 + -0.48x + x2 = 0.04 + 0.0576 Combine like terms: 0.04 + 0.0576 = 0.0976 0.0576 + -0.48x + x2 = 0.0976 Factor a perfect square on the left side: (x + -0.24)(x + -0.24) = 0.0976 Calculate the square root of the right side: 0.312409987 Break this problem into two subproblems by setting (x + -0.24) equal to 0.312409987 and -0.312409987.Subproblem 1
x + -0.24 = 0.312409987 Simplifying x + -0.24 = 0.312409987 Reorder the terms: -0.24 + x = 0.312409987 Solving -0.24 + x = 0.312409987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.24' to each side of the equation. -0.24 + 0.24 + x = 0.312409987 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + x = 0.312409987 + 0.24 x = 0.312409987 + 0.24 Combine like terms: 0.312409987 + 0.24 = 0.552409987 x = 0.552409987 Simplifying x = 0.552409987Subproblem 2
x + -0.24 = -0.312409987 Simplifying x + -0.24 = -0.312409987 Reorder the terms: -0.24 + x = -0.312409987 Solving -0.24 + x = -0.312409987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.24' to each side of the equation. -0.24 + 0.24 + x = -0.312409987 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + x = -0.312409987 + 0.24 x = -0.312409987 + 0.24 Combine like terms: -0.312409987 + 0.24 = -0.072409987 x = -0.072409987 Simplifying x = -0.072409987Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.552409987, -0.072409987}
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