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Simplifying 2m2 + -7m + -23 = -10 Reorder the terms: -23 + -7m + 2m2 = -10 Solving -23 + -7m + 2m2 = -10 Solving for variable 'm'. Reorder the terms: -23 + 10 + -7m + 2m2 = -10 + 10 Combine like terms: -23 + 10 = -13 -13 + -7m + 2m2 = -10 + 10 Combine like terms: -10 + 10 = 0 -13 + -7m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + -3.5m + m2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -3.5m + 6.5 + m2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -3.5m + m2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -3.5m + m2 = 0 + 6.5 -3.5m + m2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -3.5m + m2 = 6.5 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 = 6.5 + 3.0625 Reorder the terms: 3.0625 + -3.5m + m2 = 6.5 + 3.0625 Combine like terms: 6.5 + 3.0625 = 9.5625 3.0625 + -3.5m + m2 = 9.5625 Factor a perfect square on the left side: (m + -1.75)(m + -1.75) = 9.5625 Calculate the square root of the right side: 3.092329219 Break this problem into two subproblems by setting (m + -1.75) equal to 3.092329219 and -3.092329219.Subproblem 1
m + -1.75 = 3.092329219 Simplifying m + -1.75 = 3.092329219 Reorder the terms: -1.75 + m = 3.092329219 Solving -1.75 + m = 3.092329219 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 = 3.092329219 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + m = 3.092329219 + 1.75 m = 3.092329219 + 1.75 Combine like terms: 3.092329219 + 1.75 = 4.842329219 m = 4.842329219 Simplifying m = 4.842329219Subproblem 2
m + -1.75 = -3.092329219 Simplifying m + -1.75 = -3.092329219 Reorder the terms: -1.75 + m = -3.092329219 Solving -1.75 + m = -3.092329219 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 = -3.092329219 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + m = -3.092329219 + 1.75 m = -3.092329219 + 1.75 Combine like terms: -3.092329219 + 1.75 = -1.342329219 m = -1.342329219 Simplifying m = -1.342329219Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.842329219, -1.342329219}
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