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Simplifying 6x2 + 5x + -24 = 0 Reorder the terms: -24 + 5x + 6x2 = 0 Solving -24 + 5x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.8333333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.8333333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.8333333333x + x2 = 0 + 4 0.8333333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.8333333333x + x2 = 4 The x term is 0.8333333333x. Take half its coefficient (0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. 0.8333333333x + 0.1736111111 + x2 = 4 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 4 + 0.1736111111 Combine like terms: 4 + 0.1736111111 = 4.1736111111 0.1736111111 + 0.8333333333x + x2 = 4.1736111111 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 4.1736111111 Calculate the square root of the right side: 2.042941779 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 2.042941779 and -2.042941779.Subproblem 1
x + 0.4166666667 = 2.042941779 Simplifying x + 0.4166666667 = 2.042941779 Reorder the terms: 0.4166666667 + x = 2.042941779 Solving 0.4166666667 + x = 2.042941779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 2.042941779 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 2.042941779 + -0.4166666667 x = 2.042941779 + -0.4166666667 Combine like terms: 2.042941779 + -0.4166666667 = 1.6262751123 x = 1.6262751123 Simplifying x = 1.6262751123Subproblem 2
x + 0.4166666667 = -2.042941779 Simplifying x + 0.4166666667 = -2.042941779 Reorder the terms: 0.4166666667 + x = -2.042941779 Solving 0.4166666667 + x = -2.042941779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -2.042941779 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -2.042941779 + -0.4166666667 x = -2.042941779 + -0.4166666667 Combine like terms: -2.042941779 + -0.4166666667 = -2.4596084457 x = -2.4596084457 Simplifying x = -2.4596084457Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6262751123, -2.4596084457}
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