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Simplifying 5m2 + 3m + -21 = 0 Reorder the terms: -21 + 3m + 5m2 = 0 Solving -21 + 3m + 5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + 0.6m + m2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 0.6m + 4.2 + m2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 0.6m + m2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 0.6m + m2 = 0 + 4.2 0.6m + m2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 0.6m + m2 = 4.2 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 = 4.2 + 0.09 Reorder the terms: 0.09 + 0.6m + m2 = 4.2 + 0.09 Combine like terms: 4.2 + 0.09 = 4.29 0.09 + 0.6m + m2 = 4.29 Factor a perfect square on the left side: (m + 0.3)(m + 0.3) = 4.29 Calculate the square root of the right side: 2.071231518 Break this problem into two subproblems by setting (m + 0.3) equal to 2.071231518 and -2.071231518.Subproblem 1
m + 0.3 = 2.071231518 Simplifying m + 0.3 = 2.071231518 Reorder the terms: 0.3 + m = 2.071231518 Solving 0.3 + m = 2.071231518 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 = 2.071231518 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + m = 2.071231518 + -0.3 m = 2.071231518 + -0.3 Combine like terms: 2.071231518 + -0.3 = 1.771231518 m = 1.771231518 Simplifying m = 1.771231518Subproblem 2
m + 0.3 = -2.071231518 Simplifying m + 0.3 = -2.071231518 Reorder the terms: 0.3 + m = -2.071231518 Solving 0.3 + m = -2.071231518 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 = -2.071231518 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + m = -2.071231518 + -0.3 m = -2.071231518 + -0.3 Combine like terms: -2.071231518 + -0.3 = -2.371231518 m = -2.371231518 Simplifying m = -2.371231518Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.771231518, -2.371231518}
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