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Simplifying 5m2 + 31m + -24 = 0 Reorder the terms: -24 + 31m + 5m2 = 0 Solving -24 + 31m + 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'. -4.8 + 6.2m + m2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + 6.2m + 4.8 + m2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + 6.2m + m2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 6.2m + m2 = 0 + 4.8 6.2m + m2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 6.2m + m2 = 4.8 The m term is 6.2m. Take half its coefficient (3.1). Square it (9.61) and add it to both sides. Add '9.61' to each side of the equation. 6.2m + 9.61 + m2 = 4.8 + 9.61 Reorder the terms: 9.61 + 6.2m + m2 = 4.8 + 9.61 Combine like terms: 4.8 + 9.61 = 14.41 9.61 + 6.2m + m2 = 14.41 Factor a perfect square on the left side: (m + 3.1)(m + 3.1) = 14.41 Calculate the square root of the right side: 3.796050579 Break this problem into two subproblems by setting (m + 3.1) equal to 3.796050579 and -3.796050579.Subproblem 1
m + 3.1 = 3.796050579 Simplifying m + 3.1 = 3.796050579 Reorder the terms: 3.1 + m = 3.796050579 Solving 3.1 + m = 3.796050579 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + m = 3.796050579 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + m = 3.796050579 + -3.1 m = 3.796050579 + -3.1 Combine like terms: 3.796050579 + -3.1 = 0.696050579 m = 0.696050579 Simplifying m = 0.696050579Subproblem 2
m + 3.1 = -3.796050579 Simplifying m + 3.1 = -3.796050579 Reorder the terms: 3.1 + m = -3.796050579 Solving 3.1 + m = -3.796050579 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.1' to each side of the equation. 3.1 + -3.1 + m = -3.796050579 + -3.1 Combine like terms: 3.1 + -3.1 = 0.0 0.0 + m = -3.796050579 + -3.1 m = -3.796050579 + -3.1 Combine like terms: -3.796050579 + -3.1 = -6.896050579 m = -6.896050579 Simplifying m = -6.896050579Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.696050579, -6.896050579}
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