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Simplifying 7m2 + -18 = 3m Reorder the terms: -18 + 7m2 = 3m Solving -18 + 7m2 = 3m Solving for variable 'm'. Reorder the terms: -18 + -3m + 7m2 = 3m + -3m Combine like terms: 3m + -3m = 0 -18 + -3m + 7m2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.571428571 + -0.4285714286m + m2 = 0 Move the constant term to the right: Add '2.571428571' to each side of the equation. -2.571428571 + -0.4285714286m + 2.571428571 + m2 = 0 + 2.571428571 Reorder the terms: -2.571428571 + 2.571428571 + -0.4285714286m + m2 = 0 + 2.571428571 Combine like terms: -2.571428571 + 2.571428571 = 0.000000000 0.000000000 + -0.4285714286m + m2 = 0 + 2.571428571 -0.4285714286m + m2 = 0 + 2.571428571 Combine like terms: 0 + 2.571428571 = 2.571428571 -0.4285714286m + m2 = 2.571428571 The m term is -0.4285714286m. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286m + 0.04591836735 + m2 = 2.571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286m + m2 = 2.571428571 + 0.04591836735 Combine like terms: 2.571428571 + 0.04591836735 = 2.61734693835 0.04591836735 + -0.4285714286m + m2 = 2.61734693835 Factor a perfect square on the left side: (m + -0.2142857143)(m + -0.2142857143) = 2.61734693835 Calculate the square root of the right side: 1.617821665 Break this problem into two subproblems by setting (m + -0.2142857143) equal to 1.617821665 and -1.617821665.Subproblem 1
m + -0.2142857143 = 1.617821665 Simplifying m + -0.2142857143 = 1.617821665 Reorder the terms: -0.2142857143 + m = 1.617821665 Solving -0.2142857143 + m = 1.617821665 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + m = 1.617821665 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + m = 1.617821665 + 0.2142857143 m = 1.617821665 + 0.2142857143 Combine like terms: 1.617821665 + 0.2142857143 = 1.8321073793 m = 1.8321073793 Simplifying m = 1.8321073793Subproblem 2
m + -0.2142857143 = -1.617821665 Simplifying m + -0.2142857143 = -1.617821665 Reorder the terms: -0.2142857143 + m = -1.617821665 Solving -0.2142857143 + m = -1.617821665 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + m = -1.617821665 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + m = -1.617821665 + 0.2142857143 m = -1.617821665 + 0.2142857143 Combine like terms: -1.617821665 + 0.2142857143 = -1.4035359507 m = -1.4035359507 Simplifying m = -1.4035359507Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.8321073793, -1.4035359507}
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