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Simplifying m2 + 10 = 15m Reorder the terms: 10 + m2 = 15m Solving 10 + m2 = 15m Solving for variable 'm'. Reorder the terms: 10 + -15m + m2 = 15m + -15m Combine like terms: 15m + -15m = 0 10 + -15m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -15m + -10 + m2 = 0 + -10 Reorder the terms: 10 + -10 + -15m + m2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -15m + m2 = 0 + -10 -15m + m2 = 0 + -10 Combine like terms: 0 + -10 = -10 -15m + m2 = -10 The m term is -15m. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15m + 56.25 + m2 = -10 + 56.25 Reorder the terms: 56.25 + -15m + m2 = -10 + 56.25 Combine like terms: -10 + 56.25 = 46.25 56.25 + -15m + m2 = 46.25 Factor a perfect square on the left side: (m + -7.5)(m + -7.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (m + -7.5) equal to 6.800735254 and -6.800735254.Subproblem 1
m + -7.5 = 6.800735254 Simplifying m + -7.5 = 6.800735254 Reorder the terms: -7.5 + m = 6.800735254 Solving -7.5 + m = 6.800735254 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + m = 6.800735254 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + m = 6.800735254 + 7.5 m = 6.800735254 + 7.5 Combine like terms: 6.800735254 + 7.5 = 14.300735254 m = 14.300735254 Simplifying m = 14.300735254Subproblem 2
m + -7.5 = -6.800735254 Simplifying m + -7.5 = -6.800735254 Reorder the terms: -7.5 + m = -6.800735254 Solving -7.5 + m = -6.800735254 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + m = -6.800735254 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + m = -6.800735254 + 7.5 m = -6.800735254 + 7.5 Combine like terms: -6.800735254 + 7.5 = 0.699264746 m = 0.699264746 Simplifying m = 0.699264746Solution
The solution to the problem is based on the solutions from the subproblems. m = {14.300735254, 0.699264746}
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