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Simplifying -4x2 + -5.5x + 5 = 0 Reorder the terms: 5 + -5.5x + -4x2 = 0 Solving 5 + -5.5x + -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'. -1.25 + 1.375x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 1.375x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 1.375x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 1.375x + x2 = 0 + 1.25 1.375x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 1.375x + x2 = 1.25 The x term is 1.375x. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375x + 0.47265625 + x2 = 1.25 + 0.47265625 Reorder the terms: 0.47265625 + 1.375x + x2 = 1.25 + 0.47265625 Combine like terms: 1.25 + 0.47265625 = 1.72265625 0.47265625 + 1.375x + x2 = 1.72265625 Factor a perfect square on the left side: (x + 0.6875)(x + 0.6875) = 1.72265625 Calculate the square root of the right side: 1.3125 Break this problem into two subproblems by setting (x + 0.6875) equal to 1.3125 and -1.3125.Subproblem 1
x + 0.6875 = 1.3125 Simplifying x + 0.6875 = 1.3125 Reorder the terms: 0.6875 + x = 1.3125 Solving 0.6875 + x = 1.3125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = 1.3125 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = 1.3125 + -0.6875 x = 1.3125 + -0.6875 Combine like terms: 1.3125 + -0.6875 = 0.625 x = 0.625 Simplifying x = 0.625Subproblem 2
x + 0.6875 = -1.3125 Simplifying x + 0.6875 = -1.3125 Reorder the terms: 0.6875 + x = -1.3125 Solving 0.6875 + x = -1.3125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + x = -1.3125 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + x = -1.3125 + -0.6875 x = -1.3125 + -0.6875 Combine like terms: -1.3125 + -0.6875 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.625, -2}
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