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Simplifying 4x2 + -27x + 13 = 7x + 4 Reorder the terms: 13 + -27x + 4x2 = 7x + 4 Reorder the terms: 13 + -27x + 4x2 = 4 + 7x Solving 13 + -27x + 4x2 = 4 + 7x Solving for variable 'x'. Reorder the terms: 13 + -4 + -27x + -7x + 4x2 = 4 + 7x + -4 + -7x Combine like terms: 13 + -4 = 9 9 + -27x + -7x + 4x2 = 4 + 7x + -4 + -7x Combine like terms: -27x + -7x = -34x 9 + -34x + 4x2 = 4 + 7x + -4 + -7x Reorder the terms: 9 + -34x + 4x2 = 4 + -4 + 7x + -7x Combine like terms: 4 + -4 = 0 9 + -34x + 4x2 = 0 + 7x + -7x 9 + -34x + 4x2 = 7x + -7x Combine like terms: 7x + -7x = 0 9 + -34x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -8.5x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -8.5x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -8.5x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -8.5x + x2 = 0 + -2.25 -8.5x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -8.5x + x2 = -2.25 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = -2.25 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -2.25 + 18.0625 Combine like terms: -2.25 + 18.0625 = 15.8125 18.0625 + -8.5x + x2 = 15.8125 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 15.8125 Calculate the square root of the right side: 3.97649343 Break this problem into two subproblems by setting (x + -4.25) equal to 3.97649343 and -3.97649343.Subproblem 1
x + -4.25 = 3.97649343 Simplifying x + -4.25 = 3.97649343 Reorder the terms: -4.25 + x = 3.97649343 Solving -4.25 + x = 3.97649343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 3.97649343 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 3.97649343 + 4.25 x = 3.97649343 + 4.25 Combine like terms: 3.97649343 + 4.25 = 8.22649343 x = 8.22649343 Simplifying x = 8.22649343Subproblem 2
x + -4.25 = -3.97649343 Simplifying x + -4.25 = -3.97649343 Reorder the terms: -4.25 + x = -3.97649343 Solving -4.25 + x = -3.97649343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -3.97649343 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -3.97649343 + 4.25 x = -3.97649343 + 4.25 Combine like terms: -3.97649343 + 4.25 = 0.27350657 x = 0.27350657 Simplifying x = 0.27350657Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.22649343, 0.27350657}
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