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Simplifying 8m2 + 16m + 5 = 0 Reorder the terms: 5 + 16m + 8m2 = 0 Solving 5 + 16m + 8m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + 2m + m2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + 2m + -0.625 + m2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + 2m + m2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + 2m + m2 = 0 + -0.625 2m + m2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 2m + m2 = -0.625 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = -0.625 + 1 Reorder the terms: 1 + 2m + m2 = -0.625 + 1 Combine like terms: -0.625 + 1 = 0.375 1 + 2m + m2 = 0.375 Factor a perfect square on the left side: (m + 1)(m + 1) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (m + 1) equal to 0.612372436 and -0.612372436.Subproblem 1
m + 1 = 0.612372436 Simplifying m + 1 = 0.612372436 Reorder the terms: 1 + m = 0.612372436 Solving 1 + m = 0.612372436 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 0.612372436 + -1 Combine like terms: 1 + -1 = 0 0 + m = 0.612372436 + -1 m = 0.612372436 + -1 Combine like terms: 0.612372436 + -1 = -0.387627564 m = -0.387627564 Simplifying m = -0.387627564Subproblem 2
m + 1 = -0.612372436 Simplifying m + 1 = -0.612372436 Reorder the terms: 1 + m = -0.612372436 Solving 1 + m = -0.612372436 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -0.612372436 + -1 Combine like terms: 1 + -1 = 0 0 + m = -0.612372436 + -1 m = -0.612372436 + -1 Combine like terms: -0.612372436 + -1 = -1.612372436 m = -1.612372436 Simplifying m = -1.612372436Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.387627564, -1.612372436}
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