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Simplifying 12.5x2 + -5x + -11 = 0 Reorder the terms: -11 + -5x + 12.5x2 = 0 Solving -11 + -5x + 12.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12.5 the coefficient of the squared term: Divide each side by '12.5'. -0.88 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.88' to each side of the equation. -0.88 + -0.4x + 0.88 + x2 = 0 + 0.88 Reorder the terms: -0.88 + 0.88 + -0.4x + x2 = 0 + 0.88 Combine like terms: -0.88 + 0.88 = 0.00 0.00 + -0.4x + x2 = 0 + 0.88 -0.4x + x2 = 0 + 0.88 Combine like terms: 0 + 0.88 = 0.88 -0.4x + x2 = 0.88 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.88 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.88 + 0.04 Combine like terms: 0.88 + 0.04 = 0.92 0.04 + -0.4x + x2 = 0.92 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.92 Calculate the square root of the right side: 0.959166305 Break this problem into two subproblems by setting (x + -0.2) equal to 0.959166305 and -0.959166305.Subproblem 1
x + -0.2 = 0.959166305 Simplifying x + -0.2 = 0.959166305 Reorder the terms: -0.2 + x = 0.959166305 Solving -0.2 + x = 0.959166305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.959166305 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.959166305 + 0.2 x = 0.959166305 + 0.2 Combine like terms: 0.959166305 + 0.2 = 1.159166305 x = 1.159166305 Simplifying x = 1.159166305Subproblem 2
x + -0.2 = -0.959166305 Simplifying x + -0.2 = -0.959166305 Reorder the terms: -0.2 + x = -0.959166305 Solving -0.2 + x = -0.959166305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.959166305 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.959166305 + 0.2 x = -0.959166305 + 0.2 Combine like terms: -0.959166305 + 0.2 = -0.759166305 x = -0.759166305 Simplifying x = -0.759166305Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.159166305, -0.759166305}
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