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Simplifying 6x2 + -5x = 36 Reorder the terms: -5x + 6x2 = 36 Solving -5x + 6x2 = 36 Solving for variable 'x'. Reorder the terms: -36 + -5x + 6x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -0.8333333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -0.8333333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -0.8333333333x + x2 = 0 + 6 -0.8333333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -0.8333333333x + x2 = 6 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 = 6 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x + x2 = 6 + 0.1736111111 Combine like terms: 6 + 0.1736111111 = 6.1736111111 0.1736111111 + -0.8333333333x + x2 = 6.1736111111 Factor a perfect square on the left side: (x + -0.4166666667)(x + -0.4166666667) = 6.1736111111 Calculate the square root of the right side: 2.484675253 Break this problem into two subproblems by setting (x + -0.4166666667) equal to 2.484675253 and -2.484675253.Subproblem 1
x + -0.4166666667 = 2.484675253 Simplifying x + -0.4166666667 = 2.484675253 Reorder the terms: -0.4166666667 + x = 2.484675253 Solving -0.4166666667 + x = 2.484675253 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 = 2.484675253 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = 2.484675253 + 0.4166666667 x = 2.484675253 + 0.4166666667 Combine like terms: 2.484675253 + 0.4166666667 = 2.9013419197 x = 2.9013419197 Simplifying x = 2.9013419197Subproblem 2
x + -0.4166666667 = -2.484675253 Simplifying x + -0.4166666667 = -2.484675253 Reorder the terms: -0.4166666667 + x = -2.484675253 Solving -0.4166666667 + x = -2.484675253 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 = -2.484675253 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x = -2.484675253 + 0.4166666667 x = -2.484675253 + 0.4166666667 Combine like terms: -2.484675253 + 0.4166666667 = -2.0680085863 x = -2.0680085863 Simplifying x = -2.0680085863Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9013419197, -2.0680085863}
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