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Simplifying m2 + -15m + 9 = 0 Reorder the terms: 9 + -15m + m2 = 0 Solving 9 + -15m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -15m + -9 + m2 = 0 + -9 Reorder the terms: 9 + -9 + -15m + m2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -15m + m2 = 0 + -9 -15m + m2 = 0 + -9 Combine like terms: 0 + -9 = -9 -15m + m2 = -9 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 = -9 + 56.25 Reorder the terms: 56.25 + -15m + m2 = -9 + 56.25 Combine like terms: -9 + 56.25 = 47.25 56.25 + -15m + m2 = 47.25 Factor a perfect square on the left side: (m + -7.5)(m + -7.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (m + -7.5) equal to 6.873863542 and -6.873863542.Subproblem 1
m + -7.5 = 6.873863542 Simplifying m + -7.5 = 6.873863542 Reorder the terms: -7.5 + m = 6.873863542 Solving -7.5 + m = 6.873863542 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 = 6.873863542 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + m = 6.873863542 + 7.5 m = 6.873863542 + 7.5 Combine like terms: 6.873863542 + 7.5 = 14.373863542 m = 14.373863542 Simplifying m = 14.373863542Subproblem 2
m + -7.5 = -6.873863542 Simplifying m + -7.5 = -6.873863542 Reorder the terms: -7.5 + m = -6.873863542 Solving -7.5 + m = -6.873863542 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 = -6.873863542 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + m = -6.873863542 + 7.5 m = -6.873863542 + 7.5 Combine like terms: -6.873863542 + 7.5 = 0.626136458 m = 0.626136458 Simplifying m = 0.626136458Solution
The solution to the problem is based on the solutions from the subproblems. m = {14.373863542, 0.626136458}
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