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Simplifying 2m2 + 5m + -21 = 0 Reorder the terms: -21 + 5m + 2m2 = 0 Solving -21 + 5m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + 2.5m + m2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 2.5m + 10.5 + m2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 2.5m + m2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 2.5m + m2 = 0 + 10.5 2.5m + m2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 2.5m + m2 = 10.5 The m term is 2.5m. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5m + 1.5625 + m2 = 10.5 + 1.5625 Reorder the terms: 1.5625 + 2.5m + m2 = 10.5 + 1.5625 Combine like terms: 10.5 + 1.5625 = 12.0625 1.5625 + 2.5m + m2 = 12.0625 Factor a perfect square on the left side: (m + 1.25)(m + 1.25) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (m + 1.25) equal to 3.473110997 and -3.473110997.Subproblem 1
m + 1.25 = 3.473110997 Simplifying m + 1.25 = 3.473110997 Reorder the terms: 1.25 + m = 3.473110997 Solving 1.25 + m = 3.473110997 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + m = 3.473110997 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = 3.473110997 + -1.25 m = 3.473110997 + -1.25 Combine like terms: 3.473110997 + -1.25 = 2.223110997 m = 2.223110997 Simplifying m = 2.223110997Subproblem 2
m + 1.25 = -3.473110997 Simplifying m + 1.25 = -3.473110997 Reorder the terms: 1.25 + m = -3.473110997 Solving 1.25 + m = -3.473110997 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + m = -3.473110997 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = -3.473110997 + -1.25 m = -3.473110997 + -1.25 Combine like terms: -3.473110997 + -1.25 = -4.723110997 m = -4.723110997 Simplifying m = -4.723110997Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.223110997, -4.723110997}
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