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Simplifying 6m(m + 4) = m + -5 Reorder the terms: 6m(4 + m) = m + -5 (4 * 6m + m * 6m) = m + -5 (24m + 6m2) = m + -5 Reorder the terms: 24m + 6m2 = -5 + m Solving 24m + 6m2 = -5 + m Solving for variable 'm'. Reorder the terms: 5 + 24m + -1m + 6m2 = -5 + m + 5 + -1m Combine like terms: 24m + -1m = 23m 5 + 23m + 6m2 = -5 + m + 5 + -1m Reorder the terms: 5 + 23m + 6m2 = -5 + 5 + m + -1m Combine like terms: -5 + 5 = 0 5 + 23m + 6m2 = 0 + m + -1m 5 + 23m + 6m2 = m + -1m Combine like terms: m + -1m = 0 5 + 23m + 6m2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 3.833333333m + m2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 3.833333333m + -0.8333333333 + m2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 3.833333333m + m2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 3.833333333m + m2 = 0 + -0.8333333333 3.833333333m + m2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 3.833333333m + m2 = -0.8333333333 The m term is 3.833333333m. Take half its coefficient (1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. 3.833333333m + 3.673611112 + m2 = -0.8333333333 + 3.673611112 Reorder the terms: 3.673611112 + 3.833333333m + m2 = -0.8333333333 + 3.673611112 Combine like terms: -0.8333333333 + 3.673611112 = 2.8402777787 3.673611112 + 3.833333333m + m2 = 2.8402777787 Factor a perfect square on the left side: (m + 1.916666667)(m + 1.916666667) = 2.8402777787 Calculate the square root of the right side: 1.685312368 Break this problem into two subproblems by setting (m + 1.916666667) equal to 1.685312368 and -1.685312368.Subproblem 1
m + 1.916666667 = 1.685312368 Simplifying m + 1.916666667 = 1.685312368 Reorder the terms: 1.916666667 + m = 1.685312368 Solving 1.916666667 + m = 1.685312368 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + m = 1.685312368 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + m = 1.685312368 + -1.916666667 m = 1.685312368 + -1.916666667 Combine like terms: 1.685312368 + -1.916666667 = -0.231354299 m = -0.231354299 Simplifying m = -0.231354299Subproblem 2
m + 1.916666667 = -1.685312368 Simplifying m + 1.916666667 = -1.685312368 Reorder the terms: 1.916666667 + m = -1.685312368 Solving 1.916666667 + m = -1.685312368 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.916666667' to each side of the equation. 1.916666667 + -1.916666667 + m = -1.685312368 + -1.916666667 Combine like terms: 1.916666667 + -1.916666667 = 0.000000000 0.000000000 + m = -1.685312368 + -1.916666667 m = -1.685312368 + -1.916666667 Combine like terms: -1.685312368 + -1.916666667 = -3.601979035 m = -3.601979035 Simplifying m = -3.601979035Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.231354299, -3.601979035}
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