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Simplifying 0 = 4x2 + -55x + 177 Reorder the terms: 0 = 177 + -55x + 4x2 Solving 0 = 177 + -55x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -177 = -177 -177 + 55x + -4x2 = 177 + -55x + 4x2 + -177 + 55x + -4x2 Reorder the terms: -177 + 55x + -4x2 = 177 + -177 + -55x + 55x + 4x2 + -4x2 Combine like terms: 177 + -177 = 0 -177 + 55x + -4x2 = 0 + -55x + 55x + 4x2 + -4x2 -177 + 55x + -4x2 = -55x + 55x + 4x2 + -4x2 Combine like terms: -55x + 55x = 0 -177 + 55x + -4x2 = 0 + 4x2 + -4x2 -177 + 55x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -177 + 55x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 44.25 + -13.75x + x2 = 0 Move the constant term to the right: Add '-44.25' to each side of the equation. 44.25 + -13.75x + -44.25 + x2 = 0 + -44.25 Reorder the terms: 44.25 + -44.25 + -13.75x + x2 = 0 + -44.25 Combine like terms: 44.25 + -44.25 = 0.00 0.00 + -13.75x + x2 = 0 + -44.25 -13.75x + x2 = 0 + -44.25 Combine like terms: 0 + -44.25 = -44.25 -13.75x + x2 = -44.25 The x term is -13.75x. Take half its coefficient (-6.875). Square it (47.265625) and add it to both sides. Add '47.265625' to each side of the equation. -13.75x + 47.265625 + x2 = -44.25 + 47.265625 Reorder the terms: 47.265625 + -13.75x + x2 = -44.25 + 47.265625 Combine like terms: -44.25 + 47.265625 = 3.015625 47.265625 + -13.75x + x2 = 3.015625 Factor a perfect square on the left side: (x + -6.875)(x + -6.875) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (x + -6.875) equal to 1.736555499 and -1.736555499.Subproblem 1
x + -6.875 = 1.736555499 Simplifying x + -6.875 = 1.736555499 Reorder the terms: -6.875 + x = 1.736555499 Solving -6.875 + x = 1.736555499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.875' to each side of the equation. -6.875 + 6.875 + x = 1.736555499 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + x = 1.736555499 + 6.875 x = 1.736555499 + 6.875 Combine like terms: 1.736555499 + 6.875 = 8.611555499 x = 8.611555499 Simplifying x = 8.611555499Subproblem 2
x + -6.875 = -1.736555499 Simplifying x + -6.875 = -1.736555499 Reorder the terms: -6.875 + x = -1.736555499 Solving -6.875 + x = -1.736555499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.875' to each side of the equation. -6.875 + 6.875 + x = -1.736555499 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + x = -1.736555499 + 6.875 x = -1.736555499 + 6.875 Combine like terms: -1.736555499 + 6.875 = 5.138444501 x = 5.138444501 Simplifying x = 5.138444501Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.611555499, 5.138444501}
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