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Simplifying 4x2 + 12x2 + -9x + -27 = 0 Reorder the terms: -27 + -9x + 4x2 + 12x2 = 0 Combine like terms: 4x2 + 12x2 = 16x2 -27 + -9x + 16x2 = 0 Solving -27 + -9x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.6875 + -0.5625x + x2 = 0 Move the constant term to the right: Add '1.6875' to each side of the equation. -1.6875 + -0.5625x + 1.6875 + x2 = 0 + 1.6875 Reorder the terms: -1.6875 + 1.6875 + -0.5625x + x2 = 0 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + -0.5625x + x2 = 0 + 1.6875 -0.5625x + x2 = 0 + 1.6875 Combine like terms: 0 + 1.6875 = 1.6875 -0.5625x + x2 = 1.6875 The x term is -0.5625x. Take half its coefficient (-0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. -0.5625x + 0.0791015625 + x2 = 1.6875 + 0.0791015625 Reorder the terms: 0.0791015625 + -0.5625x + x2 = 1.6875 + 0.0791015625 Combine like terms: 1.6875 + 0.0791015625 = 1.7666015625 0.0791015625 + -0.5625x + x2 = 1.7666015625 Factor a perfect square on the left side: (x + -0.28125)(x + -0.28125) = 1.7666015625 Calculate the square root of the right side: 1.329135645 Break this problem into two subproblems by setting (x + -0.28125) equal to 1.329135645 and -1.329135645.Subproblem 1
x + -0.28125 = 1.329135645 Simplifying x + -0.28125 = 1.329135645 Reorder the terms: -0.28125 + x = 1.329135645 Solving -0.28125 + x = 1.329135645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = 1.329135645 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = 1.329135645 + 0.28125 x = 1.329135645 + 0.28125 Combine like terms: 1.329135645 + 0.28125 = 1.610385645 x = 1.610385645 Simplifying x = 1.610385645Subproblem 2
x + -0.28125 = -1.329135645 Simplifying x + -0.28125 = -1.329135645 Reorder the terms: -0.28125 + x = -1.329135645 Solving -0.28125 + x = -1.329135645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = -1.329135645 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = -1.329135645 + 0.28125 x = -1.329135645 + 0.28125 Combine like terms: -1.329135645 + 0.28125 = -1.047885645 x = -1.047885645 Simplifying x = -1.047885645Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.610385645, -1.047885645}
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