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Simplifying 7m2 + -6m + -30 = 0 Reorder the terms: -30 + -6m + 7m2 = 0 Solving -30 + -6m + 7m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.285714286 + -0.8571428571m + m2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + -0.8571428571m + 4.285714286 + m2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + -0.8571428571m + m2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + -0.8571428571m + m2 = 0 + 4.285714286 -0.8571428571m + m2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 -0.8571428571m + m2 = 4.285714286 The m term is -0.8571428571m. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571m + 0.1836734694 + m2 = 4.285714286 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571m + m2 = 4.285714286 + 0.1836734694 Combine like terms: 4.285714286 + 0.1836734694 = 4.4693877554 0.1836734694 + -0.8571428571m + m2 = 4.4693877554 Factor a perfect square on the left side: (m + -0.4285714286)(m + -0.4285714286) = 4.4693877554 Calculate the square root of the right side: 2.114092655 Break this problem into two subproblems by setting (m + -0.4285714286) equal to 2.114092655 and -2.114092655.Subproblem 1
m + -0.4285714286 = 2.114092655 Simplifying m + -0.4285714286 = 2.114092655 Reorder the terms: -0.4285714286 + m = 2.114092655 Solving -0.4285714286 + m = 2.114092655 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + m = 2.114092655 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + m = 2.114092655 + 0.4285714286 m = 2.114092655 + 0.4285714286 Combine like terms: 2.114092655 + 0.4285714286 = 2.5426640836 m = 2.5426640836 Simplifying m = 2.5426640836Subproblem 2
m + -0.4285714286 = -2.114092655 Simplifying m + -0.4285714286 = -2.114092655 Reorder the terms: -0.4285714286 + m = -2.114092655 Solving -0.4285714286 + m = -2.114092655 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + m = -2.114092655 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + m = -2.114092655 + 0.4285714286 m = -2.114092655 + 0.4285714286 Combine like terms: -2.114092655 + 0.4285714286 = -1.6855212264 m = -1.6855212264 Simplifying m = -1.6855212264Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.5426640836, -1.6855212264}
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