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Simplifying 2m2 + -7m + -13 = 4 Reorder the terms: -13 + -7m + 2m2 = 4 Solving -13 + -7m + 2m2 = 4 Solving for variable 'm'. Reorder the terms: -13 + -4 + -7m + 2m2 = 4 + -4 Combine like terms: -13 + -4 = -17 -17 + -7m + 2m2 = 4 + -4 Combine like terms: 4 + -4 = 0 -17 + -7m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + -3.5m + m2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -3.5m + 8.5 + m2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -3.5m + m2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -3.5m + m2 = 0 + 8.5 -3.5m + m2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -3.5m + m2 = 8.5 The m term is -3.5m. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5m + 3.0625 + m2 = 8.5 + 3.0625 Reorder the terms: 3.0625 + -3.5m + m2 = 8.5 + 3.0625 Combine like terms: 8.5 + 3.0625 = 11.5625 3.0625 + -3.5m + m2 = 11.5625 Factor a perfect square on the left side: (m + -1.75)(m + -1.75) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (m + -1.75) equal to 3.400367627 and -3.400367627.Subproblem 1
m + -1.75 = 3.400367627 Simplifying m + -1.75 = 3.400367627 Reorder the terms: -1.75 + m = 3.400367627 Solving -1.75 + m = 3.400367627 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + m = 3.400367627 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + m = 3.400367627 + 1.75 m = 3.400367627 + 1.75 Combine like terms: 3.400367627 + 1.75 = 5.150367627 m = 5.150367627 Simplifying m = 5.150367627Subproblem 2
m + -1.75 = -3.400367627 Simplifying m + -1.75 = -3.400367627 Reorder the terms: -1.75 + m = -3.400367627 Solving -1.75 + m = -3.400367627 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + m = -3.400367627 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + m = -3.400367627 + 1.75 m = -3.400367627 + 1.75 Combine like terms: -3.400367627 + 1.75 = -1.650367627 m = -1.650367627 Simplifying m = -1.650367627Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.150367627, -1.650367627}
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