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Simplifying 3m2 + -10 = 6m Reorder the terms: -10 + 3m2 = 6m Solving -10 + 3m2 = 6m Solving for variable 'm'. Reorder the terms: -10 + -6m + 3m2 = 6m + -6m Combine like terms: 6m + -6m = 0 -10 + -6m + 3m2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + -2m + m2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -2m + 3.333333333 + m2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -2m + m2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -2m + m2 = 0 + 3.333333333 -2m + m2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -2m + m2 = 3.333333333 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 = 3.333333333 + 1 Reorder the terms: 1 + -2m + m2 = 3.333333333 + 1 Combine like terms: 3.333333333 + 1 = 4.333333333 1 + -2m + m2 = 4.333333333 Factor a perfect square on the left side: (m + -1)(m + -1) = 4.333333333 Calculate the square root of the right side: 2.081665999 Break this problem into two subproblems by setting (m + -1) equal to 2.081665999 and -2.081665999.Subproblem 1
m + -1 = 2.081665999 Simplifying m + -1 = 2.081665999 Reorder the terms: -1 + m = 2.081665999 Solving -1 + m = 2.081665999 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 = 2.081665999 + 1 Combine like terms: -1 + 1 = 0 0 + m = 2.081665999 + 1 m = 2.081665999 + 1 Combine like terms: 2.081665999 + 1 = 3.081665999 m = 3.081665999 Simplifying m = 3.081665999Subproblem 2
m + -1 = -2.081665999 Simplifying m + -1 = -2.081665999 Reorder the terms: -1 + m = -2.081665999 Solving -1 + m = -2.081665999 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 = -2.081665999 + 1 Combine like terms: -1 + 1 = 0 0 + m = -2.081665999 + 1 m = -2.081665999 + 1 Combine like terms: -2.081665999 + 1 = -1.081665999 m = -1.081665999 Simplifying m = -1.081665999Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.081665999, -1.081665999}
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