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Simplifying 4m2 + -9 = -10m Reorder the terms: -9 + 4m2 = -10m Solving -9 + 4m2 = -10m Solving for variable 'm'. Reorder the terms: -9 + 10m + 4m2 = -10m + 10m Combine like terms: -10m + 10m = 0 -9 + 10m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 2.5m + m2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 2.5m + 2.25 + m2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 2.5m + m2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 2.5m + m2 = 0 + 2.25 2.5m + m2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 2.5m + m2 = 2.25 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 = 2.25 + 1.5625 Reorder the terms: 1.5625 + 2.5m + m2 = 2.25 + 1.5625 Combine like terms: 2.25 + 1.5625 = 3.8125 1.5625 + 2.5m + m2 = 3.8125 Factor a perfect square on the left side: (m + 1.25)(m + 1.25) = 3.8125 Calculate the square root of the right side: 1.952562419 Break this problem into two subproblems by setting (m + 1.25) equal to 1.952562419 and -1.952562419.Subproblem 1
m + 1.25 = 1.952562419 Simplifying m + 1.25 = 1.952562419 Reorder the terms: 1.25 + m = 1.952562419 Solving 1.25 + m = 1.952562419 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 = 1.952562419 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = 1.952562419 + -1.25 m = 1.952562419 + -1.25 Combine like terms: 1.952562419 + -1.25 = 0.702562419 m = 0.702562419 Simplifying m = 0.702562419Subproblem 2
m + 1.25 = -1.952562419 Simplifying m + 1.25 = -1.952562419 Reorder the terms: 1.25 + m = -1.952562419 Solving 1.25 + m = -1.952562419 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 = -1.952562419 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = -1.952562419 + -1.25 m = -1.952562419 + -1.25 Combine like terms: -1.952562419 + -1.25 = -3.202562419 m = -3.202562419 Simplifying m = -3.202562419Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.702562419, -3.202562419}
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