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Simplifying 4x2 + -23x + 27 = 0 Reorder the terms: 27 + -23x + 4x2 = 0 Solving 27 + -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'. 6.75 + -5.75x + x2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + -5.75x + -6.75 + x2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + -5.75x + x2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + -5.75x + x2 = 0 + -6.75 -5.75x + x2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 -5.75x + x2 = -6.75 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 = -6.75 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = -6.75 + 8.265625 Combine like terms: -6.75 + 8.265625 = 1.515625 8.265625 + -5.75x + x2 = 1.515625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + -2.875) equal to 1.231107225 and -1.231107225.Subproblem 1
x + -2.875 = 1.231107225 Simplifying x + -2.875 = 1.231107225 Reorder the terms: -2.875 + x = 1.231107225 Solving -2.875 + x = 1.231107225 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 = 1.231107225 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 1.231107225 + 2.875 x = 1.231107225 + 2.875 Combine like terms: 1.231107225 + 2.875 = 4.106107225 x = 4.106107225 Simplifying x = 4.106107225Subproblem 2
x + -2.875 = -1.231107225 Simplifying x + -2.875 = -1.231107225 Reorder the terms: -2.875 + x = -1.231107225 Solving -2.875 + x = -1.231107225 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 = -1.231107225 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -1.231107225 + 2.875 x = -1.231107225 + 2.875 Combine like terms: -1.231107225 + 2.875 = 1.643892775 x = 1.643892775 Simplifying x = 1.643892775Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.106107225, 1.643892775}
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