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Simplifying 4x2 + 27x = 12 Reorder the terms: 27x + 4x2 = 12 Solving 27x + 4x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 27x + 4x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 27x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + 6.75x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 6.75x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 6.75x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6.75x + x2 = 0 + 3 6.75x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 6.75x + x2 = 3 The x term is 6.75x. Take half its coefficient (3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. 6.75x + 11.390625 + x2 = 3 + 11.390625 Reorder the terms: 11.390625 + 6.75x + x2 = 3 + 11.390625 Combine like terms: 3 + 11.390625 = 14.390625 11.390625 + 6.75x + x2 = 14.390625 Factor a perfect square on the left side: (x + 3.375)(x + 3.375) = 14.390625 Calculate the square root of the right side: 3.793497726 Break this problem into two subproblems by setting (x + 3.375) equal to 3.793497726 and -3.793497726.Subproblem 1
x + 3.375 = 3.793497726 Simplifying x + 3.375 = 3.793497726 Reorder the terms: 3.375 + x = 3.793497726 Solving 3.375 + x = 3.793497726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = 3.793497726 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = 3.793497726 + -3.375 x = 3.793497726 + -3.375 Combine like terms: 3.793497726 + -3.375 = 0.418497726 x = 0.418497726 Simplifying x = 0.418497726Subproblem 2
x + 3.375 = -3.793497726 Simplifying x + 3.375 = -3.793497726 Reorder the terms: 3.375 + x = -3.793497726 Solving 3.375 + x = -3.793497726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.375' to each side of the equation. 3.375 + -3.375 + x = -3.793497726 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + x = -3.793497726 + -3.375 x = -3.793497726 + -3.375 Combine like terms: -3.793497726 + -3.375 = -7.168497726 x = -7.168497726 Simplifying x = -7.168497726Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.418497726, -7.168497726}
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