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Simplifying 6x2 + 5x = 12 Reorder the terms: 5x + 6x2 = 12 Solving 5x + 6x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 5x + 6x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.8333333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.8333333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.8333333333x + x2 = 0 + 2 0.8333333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.8333333333x + x2 = 2 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 = 2 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 2 + 0.1736111111 Combine like terms: 2 + 0.1736111111 = 2.1736111111 0.1736111111 + 0.8333333333x + x2 = 2.1736111111 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 2.1736111111 Calculate the square root of the right side: 1.474317168 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 1.474317168 and -1.474317168.Subproblem 1
x + 0.4166666667 = 1.474317168 Simplifying x + 0.4166666667 = 1.474317168 Reorder the terms: 0.4166666667 + x = 1.474317168 Solving 0.4166666667 + x = 1.474317168 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 = 1.474317168 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 1.474317168 + -0.4166666667 x = 1.474317168 + -0.4166666667 Combine like terms: 1.474317168 + -0.4166666667 = 1.0576505013 x = 1.0576505013 Simplifying x = 1.0576505013Subproblem 2
x + 0.4166666667 = -1.474317168 Simplifying x + 0.4166666667 = -1.474317168 Reorder the terms: 0.4166666667 + x = -1.474317168 Solving 0.4166666667 + x = -1.474317168 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 = -1.474317168 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -1.474317168 + -0.4166666667 x = -1.474317168 + -0.4166666667 Combine like terms: -1.474317168 + -0.4166666667 = -1.8909838347 x = -1.8909838347 Simplifying x = -1.8909838347Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0576505013, -1.8909838347}
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