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Simplifying 12x2 + 43x + -24 = 0 Reorder the terms: -24 + 43x + 12x2 = 0 Solving -24 + 43x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2 + 3.583333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 3.583333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 3.583333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3.583333333x + x2 = 0 + 2 3.583333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 3.583333333x + x2 = 2 The x term is 3.583333333x. Take half its coefficient (1.791666667). Square it (3.210069446) and add it to both sides. Add '3.210069446' to each side of the equation. 3.583333333x + 3.210069446 + x2 = 2 + 3.210069446 Reorder the terms: 3.210069446 + 3.583333333x + x2 = 2 + 3.210069446 Combine like terms: 2 + 3.210069446 = 5.210069446 3.210069446 + 3.583333333x + x2 = 5.210069446 Factor a perfect square on the left side: (x + 1.791666667)(x + 1.791666667) = 5.210069446 Calculate the square root of the right side: 2.282557654 Break this problem into two subproblems by setting (x + 1.791666667) equal to 2.282557654 and -2.282557654.Subproblem 1
x + 1.791666667 = 2.282557654 Simplifying x + 1.791666667 = 2.282557654 Reorder the terms: 1.791666667 + x = 2.282557654 Solving 1.791666667 + x = 2.282557654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.791666667' to each side of the equation. 1.791666667 + -1.791666667 + x = 2.282557654 + -1.791666667 Combine like terms: 1.791666667 + -1.791666667 = 0.000000000 0.000000000 + x = 2.282557654 + -1.791666667 x = 2.282557654 + -1.791666667 Combine like terms: 2.282557654 + -1.791666667 = 0.490890987 x = 0.490890987 Simplifying x = 0.490890987Subproblem 2
x + 1.791666667 = -2.282557654 Simplifying x + 1.791666667 = -2.282557654 Reorder the terms: 1.791666667 + x = -2.282557654 Solving 1.791666667 + x = -2.282557654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.791666667' to each side of the equation. 1.791666667 + -1.791666667 + x = -2.282557654 + -1.791666667 Combine like terms: 1.791666667 + -1.791666667 = 0.000000000 0.000000000 + x = -2.282557654 + -1.791666667 x = -2.282557654 + -1.791666667 Combine like terms: -2.282557654 + -1.791666667 = -4.074224321 x = -4.074224321 Simplifying x = -4.074224321Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.490890987, -4.074224321}
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