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Simplifying 3m2 + 12m + 10 = 3 Reorder the terms: 10 + 12m + 3m2 = 3 Solving 10 + 12m + 3m2 = 3 Solving for variable 'm'. Reorder the terms: 10 + -3 + 12m + 3m2 = 3 + -3 Combine like terms: 10 + -3 = 7 7 + 12m + 3m2 = 3 + -3 Combine like terms: 3 + -3 = 0 7 + 12m + 3m2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + 4m + m2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + 4m + -2.333333333 + m2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + 4m + m2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + 4m + m2 = 0 + -2.333333333 4m + m2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 4m + m2 = -2.333333333 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 = -2.333333333 + 4 Reorder the terms: 4 + 4m + m2 = -2.333333333 + 4 Combine like terms: -2.333333333 + 4 = 1.666666667 4 + 4m + m2 = 1.666666667 Factor a perfect square on the left side: (m + 2)(m + 2) = 1.666666667 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (m + 2) equal to 1.290994449 and -1.290994449.Subproblem 1
m + 2 = 1.290994449 Simplifying m + 2 = 1.290994449 Reorder the terms: 2 + m = 1.290994449 Solving 2 + m = 1.290994449 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 = 1.290994449 + -2 Combine like terms: 2 + -2 = 0 0 + m = 1.290994449 + -2 m = 1.290994449 + -2 Combine like terms: 1.290994449 + -2 = -0.709005551 m = -0.709005551 Simplifying m = -0.709005551Subproblem 2
m + 2 = -1.290994449 Simplifying m + 2 = -1.290994449 Reorder the terms: 2 + m = -1.290994449 Solving 2 + m = -1.290994449 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 = -1.290994449 + -2 Combine like terms: 2 + -2 = 0 0 + m = -1.290994449 + -2 m = -1.290994449 + -2 Combine like terms: -1.290994449 + -2 = -3.290994449 m = -3.290994449 Simplifying m = -3.290994449Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.709005551, -3.290994449}
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