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Simplifying m2 + 8m = 8 Reorder the terms: 8m + m2 = 8 Solving 8m + m2 = 8 Solving for variable 'm'. Reorder the terms: -8 + 8m + m2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 8m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 8m + 8 + m2 = 0 + 8 Reorder the terms: -8 + 8 + 8m + m2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 8m + m2 = 0 + 8 8m + m2 = 0 + 8 Combine like terms: 0 + 8 = 8 8m + m2 = 8 The m term is 8m. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8m + 16 + m2 = 8 + 16 Reorder the terms: 16 + 8m + m2 = 8 + 16 Combine like terms: 8 + 16 = 24 16 + 8m + m2 = 24 Factor a perfect square on the left side: (m + 4)(m + 4) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (m + 4) equal to 4.898979486 and -4.898979486.Subproblem 1
m + 4 = 4.898979486 Simplifying m + 4 = 4.898979486 Reorder the terms: 4 + m = 4.898979486 Solving 4 + m = 4.898979486 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + m = 4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + m = 4.898979486 + -4 m = 4.898979486 + -4 Combine like terms: 4.898979486 + -4 = 0.898979486 m = 0.898979486 Simplifying m = 0.898979486Subproblem 2
m + 4 = -4.898979486 Simplifying m + 4 = -4.898979486 Reorder the terms: 4 + m = -4.898979486 Solving 4 + m = -4.898979486 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + m = -4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + m = -4.898979486 + -4 m = -4.898979486 + -4 Combine like terms: -4.898979486 + -4 = -8.898979486 m = -8.898979486 Simplifying m = -8.898979486Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.898979486, -8.898979486}
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