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Simplifying 5m2 = 3m + 16 Reorder the terms: 5m2 = 16 + 3m Solving 5m2 = 16 + 3m Solving for variable 'm'. Reorder the terms: -16 + -3m + 5m2 = 16 + 3m + -16 + -3m Reorder the terms: -16 + -3m + 5m2 = 16 + -16 + 3m + -3m Combine like terms: 16 + -16 = 0 -16 + -3m + 5m2 = 0 + 3m + -3m -16 + -3m + 5m2 = 3m + -3m Combine like terms: 3m + -3m = 0 -16 + -3m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + -0.6m + m2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + -0.6m + 3.2 + m2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + -0.6m + m2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + -0.6m + m2 = 0 + 3.2 -0.6m + m2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 -0.6m + m2 = 3.2 The m term is -0.6m. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6m + 0.09 + m2 = 3.2 + 0.09 Reorder the terms: 0.09 + -0.6m + m2 = 3.2 + 0.09 Combine like terms: 3.2 + 0.09 = 3.29 0.09 + -0.6m + m2 = 3.29 Factor a perfect square on the left side: (m + -0.3)(m + -0.3) = 3.29 Calculate the square root of the right side: 1.813835715 Break this problem into two subproblems by setting (m + -0.3) equal to 1.813835715 and -1.813835715.Subproblem 1
m + -0.3 = 1.813835715 Simplifying m + -0.3 = 1.813835715 Reorder the terms: -0.3 + m = 1.813835715 Solving -0.3 + m = 1.813835715 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + m = 1.813835715 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + m = 1.813835715 + 0.3 m = 1.813835715 + 0.3 Combine like terms: 1.813835715 + 0.3 = 2.113835715 m = 2.113835715 Simplifying m = 2.113835715Subproblem 2
m + -0.3 = -1.813835715 Simplifying m + -0.3 = -1.813835715 Reorder the terms: -0.3 + m = -1.813835715 Solving -0.3 + m = -1.813835715 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + m = -1.813835715 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + m = -1.813835715 + 0.3 m = -1.813835715 + 0.3 Combine like terms: -1.813835715 + 0.3 = -1.513835715 m = -1.513835715 Simplifying m = -1.513835715Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.113835715, -1.513835715}
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