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Simplifying 6x2 + 5x = 30 Reorder the terms: 5x + 6x2 = 30 Solving 5x + 6x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 5x + 6x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 5x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5 + 0.8333333333x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 0.8333333333x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 0.8333333333x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 0.8333333333x + x2 = 0 + 5 0.8333333333x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 0.8333333333x + x2 = 5 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 = 5 + 0.1736111111 Reorder the terms: 0.1736111111 + 0.8333333333x + x2 = 5 + 0.1736111111 Combine like terms: 5 + 0.1736111111 = 5.1736111111 0.1736111111 + 0.8333333333x + x2 = 5.1736111111 Factor a perfect square on the left side: (x + 0.4166666667)(x + 0.4166666667) = 5.1736111111 Calculate the square root of the right side: 2.274557344 Break this problem into two subproblems by setting (x + 0.4166666667) equal to 2.274557344 and -2.274557344.Subproblem 1
x + 0.4166666667 = 2.274557344 Simplifying x + 0.4166666667 = 2.274557344 Reorder the terms: 0.4166666667 + x = 2.274557344 Solving 0.4166666667 + x = 2.274557344 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 = 2.274557344 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 2.274557344 + -0.4166666667 x = 2.274557344 + -0.4166666667 Combine like terms: 2.274557344 + -0.4166666667 = 1.8578906773 x = 1.8578906773 Simplifying x = 1.8578906773Subproblem 2
x + 0.4166666667 = -2.274557344 Simplifying x + 0.4166666667 = -2.274557344 Reorder the terms: 0.4166666667 + x = -2.274557344 Solving 0.4166666667 + x = -2.274557344 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 = -2.274557344 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -2.274557344 + -0.4166666667 x = -2.274557344 + -0.4166666667 Combine like terms: -2.274557344 + -0.4166666667 = -2.6912240107 x = -2.6912240107 Simplifying x = -2.6912240107Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8578906773, -2.6912240107}
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