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Simplifying 4x2 + 23x + -55 = 0 Reorder the terms: -55 + 23x + 4x2 = 0 Solving -55 + 23x + 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'. -13.75 + 5.75x + x2 = 0 Move the constant term to the right: Add '13.75' to each side of the equation. -13.75 + 5.75x + 13.75 + x2 = 0 + 13.75 Reorder the terms: -13.75 + 13.75 + 5.75x + x2 = 0 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + 5.75x + x2 = 0 + 13.75 5.75x + x2 = 0 + 13.75 Combine like terms: 0 + 13.75 = 13.75 5.75x + x2 = 13.75 The x term is 5.75x. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75x + 8.265625 + x2 = 13.75 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = 13.75 + 8.265625 Combine like terms: 13.75 + 8.265625 = 22.015625 8.265625 + 5.75x + x2 = 22.015625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 22.015625 Calculate the square root of the right side: 4.692081095 Break this problem into two subproblems by setting (x + 2.875) equal to 4.692081095 and -4.692081095.Subproblem 1
x + 2.875 = 4.692081095 Simplifying x + 2.875 = 4.692081095 Reorder the terms: 2.875 + x = 4.692081095 Solving 2.875 + x = 4.692081095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = 4.692081095 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 4.692081095 + -2.875 x = 4.692081095 + -2.875 Combine like terms: 4.692081095 + -2.875 = 1.817081095 x = 1.817081095 Simplifying x = 1.817081095Subproblem 2
x + 2.875 = -4.692081095 Simplifying x + 2.875 = -4.692081095 Reorder the terms: 2.875 + x = -4.692081095 Solving 2.875 + x = -4.692081095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = -4.692081095 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -4.692081095 + -2.875 x = -4.692081095 + -2.875 Combine like terms: -4.692081095 + -2.875 = -7.567081095 x = -7.567081095 Simplifying x = -7.567081095Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.817081095, -7.567081095}
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