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Simplifying 5m = 1 + m2 Solving 5m = 1 + m2 Solving for variable 'm'. Reorder the terms: -1 + 5m + -1m2 = 1 + m2 + -1 + -1m2 Reorder the terms: -1 + 5m + -1m2 = 1 + -1 + m2 + -1m2 Combine like terms: 1 + -1 = 0 -1 + 5m + -1m2 = 0 + m2 + -1m2 -1 + 5m + -1m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 -1 + 5m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -5m + m2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + -5m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5m + m2 = 0 + -1 -5m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5m + m2 = -1 The m term is -5m. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5m + 6.25 + m2 = -1 + 6.25 Reorder the terms: 6.25 + -5m + m2 = -1 + 6.25 Combine like terms: -1 + 6.25 = 5.25 6.25 + -5m + m2 = 5.25 Factor a perfect square on the left side: (m + -2.5)(m + -2.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (m + -2.5) equal to 2.291287847 and -2.291287847.Subproblem 1
m + -2.5 = 2.291287847 Simplifying m + -2.5 = 2.291287847 Reorder the terms: -2.5 + m = 2.291287847 Solving -2.5 + m = 2.291287847 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = 2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = 2.291287847 + 2.5 m = 2.291287847 + 2.5 Combine like terms: 2.291287847 + 2.5 = 4.791287847 m = 4.791287847 Simplifying m = 4.791287847Subproblem 2
m + -2.5 = -2.291287847 Simplifying m + -2.5 = -2.291287847 Reorder the terms: -2.5 + m = -2.291287847 Solving -2.5 + m = -2.291287847 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = -2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = -2.291287847 + 2.5 m = -2.291287847 + 2.5 Combine like terms: -2.291287847 + 2.5 = 0.208712153 m = 0.208712153 Simplifying m = 0.208712153Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.791287847, 0.208712153}
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