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Simplifying 7m2 + 14m + -36 = 0 Reorder the terms: -36 + 14m + 7m2 = 0 Solving -36 + 14m + 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'. -5.142857143 + 2m + m2 = 0 Move the constant term to the right: Add '5.142857143' to each side of the equation. -5.142857143 + 2m + 5.142857143 + m2 = 0 + 5.142857143 Reorder the terms: -5.142857143 + 5.142857143 + 2m + m2 = 0 + 5.142857143 Combine like terms: -5.142857143 + 5.142857143 = 0.000000000 0.000000000 + 2m + m2 = 0 + 5.142857143 2m + m2 = 0 + 5.142857143 Combine like terms: 0 + 5.142857143 = 5.142857143 2m + m2 = 5.142857143 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = 5.142857143 + 1 Reorder the terms: 1 + 2m + m2 = 5.142857143 + 1 Combine like terms: 5.142857143 + 1 = 6.142857143 1 + 2m + m2 = 6.142857143 Factor a perfect square on the left side: (m + 1)(m + 1) = 6.142857143 Calculate the square root of the right side: 2.478478796 Break this problem into two subproblems by setting (m + 1) equal to 2.478478796 and -2.478478796.Subproblem 1
m + 1 = 2.478478796 Simplifying m + 1 = 2.478478796 Reorder the terms: 1 + m = 2.478478796 Solving 1 + m = 2.478478796 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 2.478478796 + -1 Combine like terms: 1 + -1 = 0 0 + m = 2.478478796 + -1 m = 2.478478796 + -1 Combine like terms: 2.478478796 + -1 = 1.478478796 m = 1.478478796 Simplifying m = 1.478478796Subproblem 2
m + 1 = -2.478478796 Simplifying m + 1 = -2.478478796 Reorder the terms: 1 + m = -2.478478796 Solving 1 + m = -2.478478796 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -2.478478796 + -1 Combine like terms: 1 + -1 = 0 0 + m = -2.478478796 + -1 m = -2.478478796 + -1 Combine like terms: -2.478478796 + -1 = -3.478478796 m = -3.478478796 Simplifying m = -3.478478796Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.478478796, -3.478478796}
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