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Simplifying 27x + 100 = 4x2 Reorder the terms: 100 + 27x = 4x2 Solving 100 + 27x = 4x2 Solving for variable 'x'. Combine like terms: 4x2 + -4x2 = 0 100 + 27x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -25 + -6.75x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -6.75x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -6.75x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -6.75x + x2 = 0 + 25 -6.75x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -6.75x + x2 = 25 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 = 25 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = 25 + 11.390625 Combine like terms: 25 + 11.390625 = 36.390625 11.390625 + -6.75x + x2 = 36.390625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 36.390625 Calculate the square root of the right side: 6.032464256 Break this problem into two subproblems by setting (x + -3.375) equal to 6.032464256 and -6.032464256.Subproblem 1
x + -3.375 = 6.032464256 Simplifying x + -3.375 = 6.032464256 Reorder the terms: -3.375 + x = 6.032464256 Solving -3.375 + x = 6.032464256 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 = 6.032464256 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 6.032464256 + 3.375 x = 6.032464256 + 3.375 Combine like terms: 6.032464256 + 3.375 = 9.407464256 x = 9.407464256 Simplifying x = 9.407464256Subproblem 2
x + -3.375 = -6.032464256 Simplifying x + -3.375 = -6.032464256 Reorder the terms: -3.375 + x = -6.032464256 Solving -3.375 + x = -6.032464256 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 = -6.032464256 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -6.032464256 + 3.375 x = -6.032464256 + 3.375 Combine like terms: -6.032464256 + 3.375 = -2.657464256 x = -2.657464256 Simplifying x = -2.657464256Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.407464256, -2.657464256}
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