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Simplifying 8m2 + 2m = 5 Reorder the terms: 2m + 8m2 = 5 Solving 2m + 8m2 = 5 Solving for variable 'm'. Reorder the terms: -5 + 2m + 8m2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 2m + 8m2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 0.25m + m2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.25m + 0.625 + m2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.25m + m2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.25m + m2 = 0 + 0.625 0.25m + m2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.25m + m2 = 0.625 The m term is 0.25m. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25m + 0.015625 + m2 = 0.625 + 0.015625 Reorder the terms: 0.015625 + 0.25m + m2 = 0.625 + 0.015625 Combine like terms: 0.625 + 0.015625 = 0.640625 0.015625 + 0.25m + m2 = 0.640625 Factor a perfect square on the left side: (m + 0.125)(m + 0.125) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (m + 0.125) equal to 0.80039053 and -0.80039053.Subproblem 1
m + 0.125 = 0.80039053 Simplifying m + 0.125 = 0.80039053 Reorder the terms: 0.125 + m = 0.80039053 Solving 0.125 + m = 0.80039053 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + m = 0.80039053 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + m = 0.80039053 + -0.125 m = 0.80039053 + -0.125 Combine like terms: 0.80039053 + -0.125 = 0.67539053 m = 0.67539053 Simplifying m = 0.67539053Subproblem 2
m + 0.125 = -0.80039053 Simplifying m + 0.125 = -0.80039053 Reorder the terms: 0.125 + m = -0.80039053 Solving 0.125 + m = -0.80039053 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + m = -0.80039053 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + m = -0.80039053 + -0.125 m = -0.80039053 + -0.125 Combine like terms: -0.80039053 + -0.125 = -0.92539053 m = -0.92539053 Simplifying m = -0.92539053Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.67539053, -0.92539053}
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