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Simplifying 9m2 + -36m = 7 Reorder the terms: -36m + 9m2 = 7 Solving -36m + 9m2 = 7 Solving for variable 'm'. Reorder the terms: -7 + -36m + 9m2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -36m + 9m2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + -4m + m2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -4m + 0.7777777778 + m2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -4m + m2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -4m + m2 = 0 + 0.7777777778 -4m + m2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -4m + m2 = 0.7777777778 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = 0.7777777778 + 4 Reorder the terms: 4 + -4m + m2 = 0.7777777778 + 4 Combine like terms: 0.7777777778 + 4 = 4.7777777778 4 + -4m + m2 = 4.7777777778 Factor a perfect square on the left side: (m + -2)(m + -2) = 4.7777777778 Calculate the square root of the right side: 2.185812841 Break this problem into two subproblems by setting (m + -2) equal to 2.185812841 and -2.185812841.Subproblem 1
m + -2 = 2.185812841 Simplifying m + -2 = 2.185812841 Reorder the terms: -2 + m = 2.185812841 Solving -2 + m = 2.185812841 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 2.185812841 + 2 Combine like terms: -2 + 2 = 0 0 + m = 2.185812841 + 2 m = 2.185812841 + 2 Combine like terms: 2.185812841 + 2 = 4.185812841 m = 4.185812841 Simplifying m = 4.185812841Subproblem 2
m + -2 = -2.185812841 Simplifying m + -2 = -2.185812841 Reorder the terms: -2 + m = -2.185812841 Solving -2 + m = -2.185812841 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -2.185812841 + 2 Combine like terms: -2 + 2 = 0 0 + m = -2.185812841 + 2 m = -2.185812841 + 2 Combine like terms: -2.185812841 + 2 = -0.185812841 m = -0.185812841 Simplifying m = -0.185812841Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.185812841, -0.185812841}
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