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Simplifying 4x2 + 9x + -5.5 = 0 Reorder the terms: -5.5 + 9x + 4x2 = 0 Solving -5.5 + 9x + 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'. -1.375 + 2.25x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 2.25x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 2.25x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 2.25x + x2 = 0 + 1.375 2.25x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 2.25x + x2 = 1.375 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 1.375 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 1.375 + 1.265625 Combine like terms: 1.375 + 1.265625 = 2.640625 1.265625 + 2.25x + x2 = 2.640625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 2.640625 Calculate the square root of the right side: 1.625 Break this problem into two subproblems by setting (x + 1.125) equal to 1.625 and -1.625.Subproblem 1
x + 1.125 = 1.625 Simplifying x + 1.125 = 1.625 Reorder the terms: 1.125 + x = 1.625 Solving 1.125 + x = 1.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 1.625 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.625 + -1.125 x = 1.625 + -1.125 Combine like terms: 1.625 + -1.125 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 1.125 = -1.625 Simplifying x + 1.125 = -1.625 Reorder the terms: 1.125 + x = -1.625 Solving 1.125 + x = -1.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -1.625 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.625 + -1.125 x = -1.625 + -1.125 Combine like terms: -1.625 + -1.125 = -2.75 x = -2.75 Simplifying x = -2.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -2.75}
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