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Simplifying 4x2 + -87x + -41 = 0 Reorder the terms: -41 + -87x + 4x2 = 0 Solving -41 + -87x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10.25 + -21.75x + x2 = 0 Move the constant term to the right: Add '10.25' to each side of the equation. -10.25 + -21.75x + 10.25 + x2 = 0 + 10.25 Reorder the terms: -10.25 + 10.25 + -21.75x + x2 = 0 + 10.25 Combine like terms: -10.25 + 10.25 = 0.00 0.00 + -21.75x + x2 = 0 + 10.25 -21.75x + x2 = 0 + 10.25 Combine like terms: 0 + 10.25 = 10.25 -21.75x + x2 = 10.25 The x term is -21.75x. Take half its coefficient (-10.875). Square it (118.265625) and add it to both sides. Add '118.265625' to each side of the equation. -21.75x + 118.265625 + x2 = 10.25 + 118.265625 Reorder the terms: 118.265625 + -21.75x + x2 = 10.25 + 118.265625 Combine like terms: 10.25 + 118.265625 = 128.515625 118.265625 + -21.75x + x2 = 128.515625 Factor a perfect square on the left side: (x + -10.875)(x + -10.875) = 128.515625 Calculate the square root of the right side: 11.336473217 Break this problem into two subproblems by setting (x + -10.875) equal to 11.336473217 and -11.336473217.Subproblem 1
x + -10.875 = 11.336473217 Simplifying x + -10.875 = 11.336473217 Reorder the terms: -10.875 + x = 11.336473217 Solving -10.875 + x = 11.336473217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.875' to each side of the equation. -10.875 + 10.875 + x = 11.336473217 + 10.875 Combine like terms: -10.875 + 10.875 = 0.000 0.000 + x = 11.336473217 + 10.875 x = 11.336473217 + 10.875 Combine like terms: 11.336473217 + 10.875 = 22.211473217 x = 22.211473217 Simplifying x = 22.211473217Subproblem 2
x + -10.875 = -11.336473217 Simplifying x + -10.875 = -11.336473217 Reorder the terms: -10.875 + x = -11.336473217 Solving -10.875 + x = -11.336473217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.875' to each side of the equation. -10.875 + 10.875 + x = -11.336473217 + 10.875 Combine like terms: -10.875 + 10.875 = 0.000 0.000 + x = -11.336473217 + 10.875 x = -11.336473217 + 10.875 Combine like terms: -11.336473217 + 10.875 = -0.461473217 x = -0.461473217 Simplifying x = -0.461473217Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.211473217, -0.461473217}
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