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Simplifying 4x2 + -45x + 54 = 0 Reorder the terms: 54 + -45x + 4x2 = 0 Solving 54 + -45x + 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'. 13.5 + -11.25x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -11.25x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -11.25x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -11.25x + x2 = 0 + -13.5 -11.25x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -11.25x + x2 = -13.5 The x term is -11.25x. Take half its coefficient (-5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. -11.25x + 31.640625 + x2 = -13.5 + 31.640625 Reorder the terms: 31.640625 + -11.25x + x2 = -13.5 + 31.640625 Combine like terms: -13.5 + 31.640625 = 18.140625 31.640625 + -11.25x + x2 = 18.140625 Factor a perfect square on the left side: (x + -5.625)(x + -5.625) = 18.140625 Calculate the square root of the right side: 4.259181259 Break this problem into two subproblems by setting (x + -5.625) equal to 4.259181259 and -4.259181259.Subproblem 1
x + -5.625 = 4.259181259 Simplifying x + -5.625 = 4.259181259 Reorder the terms: -5.625 + x = 4.259181259 Solving -5.625 + x = 4.259181259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = 4.259181259 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = 4.259181259 + 5.625 x = 4.259181259 + 5.625 Combine like terms: 4.259181259 + 5.625 = 9.884181259 x = 9.884181259 Simplifying x = 9.884181259Subproblem 2
x + -5.625 = -4.259181259 Simplifying x + -5.625 = -4.259181259 Reorder the terms: -5.625 + x = -4.259181259 Solving -5.625 + x = -4.259181259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = -4.259181259 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = -4.259181259 + 5.625 x = -4.259181259 + 5.625 Combine like terms: -4.259181259 + 5.625 = 1.365818741 x = 1.365818741 Simplifying x = 1.365818741Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.884181259, 1.365818741}
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