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Simplifying 4x2 + -69x + 27 = 0 Reorder the terms: 27 + -69x + 4x2 = 0 Solving 27 + -69x + 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'. 6.75 + -17.25x + x2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + -17.25x + -6.75 + x2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + -17.25x + x2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + -17.25x + x2 = 0 + -6.75 -17.25x + x2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 -17.25x + x2 = -6.75 The x term is -17.25x. Take half its coefficient (-8.625). Square it (74.390625) and add it to both sides. Add '74.390625' to each side of the equation. -17.25x + 74.390625 + x2 = -6.75 + 74.390625 Reorder the terms: 74.390625 + -17.25x + x2 = -6.75 + 74.390625 Combine like terms: -6.75 + 74.390625 = 67.640625 74.390625 + -17.25x + x2 = 67.640625 Factor a perfect square on the left side: (x + -8.625)(x + -8.625) = 67.640625 Calculate the square root of the right side: 8.224392075 Break this problem into two subproblems by setting (x + -8.625) equal to 8.224392075 and -8.224392075.Subproblem 1
x + -8.625 = 8.224392075 Simplifying x + -8.625 = 8.224392075 Reorder the terms: -8.625 + x = 8.224392075 Solving -8.625 + x = 8.224392075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.625' to each side of the equation. -8.625 + 8.625 + x = 8.224392075 + 8.625 Combine like terms: -8.625 + 8.625 = 0.000 0.000 + x = 8.224392075 + 8.625 x = 8.224392075 + 8.625 Combine like terms: 8.224392075 + 8.625 = 16.849392075 x = 16.849392075 Simplifying x = 16.849392075Subproblem 2
x + -8.625 = -8.224392075 Simplifying x + -8.625 = -8.224392075 Reorder the terms: -8.625 + x = -8.224392075 Solving -8.625 + x = -8.224392075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.625' to each side of the equation. -8.625 + 8.625 + x = -8.224392075 + 8.625 Combine like terms: -8.625 + 8.625 = 0.000 0.000 + x = -8.224392075 + 8.625 x = -8.224392075 + 8.625 Combine like terms: -8.224392075 + 8.625 = 0.400607925 x = 0.400607925 Simplifying x = 0.400607925Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.849392075, 0.400607925}
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