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Simplifying (m + -6)(4m + -1) + -3(m + 3) = 0 Reorder the terms: (-6 + m)(4m + -1) + -3(m + 3) = 0 Reorder the terms: (-6 + m)(-1 + 4m) + -3(m + 3) = 0 Multiply (-6 + m) * (-1 + 4m) (-6(-1 + 4m) + m(-1 + 4m)) + -3(m + 3) = 0 ((-1 * -6 + 4m * -6) + m(-1 + 4m)) + -3(m + 3) = 0 ((6 + -24m) + m(-1 + 4m)) + -3(m + 3) = 0 (6 + -24m + (-1 * m + 4m * m)) + -3(m + 3) = 0 (6 + -24m + (-1m + 4m2)) + -3(m + 3) = 0 Combine like terms: -24m + -1m = -25m (6 + -25m + 4m2) + -3(m + 3) = 0 Reorder the terms: 6 + -25m + 4m2 + -3(3 + m) = 0 6 + -25m + 4m2 + (3 * -3 + m * -3) = 0 6 + -25m + 4m2 + (-9 + -3m) = 0 Reorder the terms: 6 + -9 + -25m + -3m + 4m2 = 0 Combine like terms: 6 + -9 = -3 -3 + -25m + -3m + 4m2 = 0 Combine like terms: -25m + -3m = -28m -3 + -28m + 4m2 = 0 Solving -3 + -28m + 4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -7m + m2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -7m + 0.75 + m2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -7m + m2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -7m + m2 = 0 + 0.75 -7m + m2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -7m + m2 = 0.75 The m term is -7m. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7m + 12.25 + m2 = 0.75 + 12.25 Reorder the terms: 12.25 + -7m + m2 = 0.75 + 12.25 Combine like terms: 0.75 + 12.25 = 13 12.25 + -7m + m2 = 13 Factor a perfect square on the left side: (m + -3.5)(m + -3.5) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (m + -3.5) equal to 3.605551275 and -3.605551275.Subproblem 1
m + -3.5 = 3.605551275 Simplifying m + -3.5 = 3.605551275 Reorder the terms: -3.5 + m = 3.605551275 Solving -3.5 + m = 3.605551275 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + m = 3.605551275 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + m = 3.605551275 + 3.5 m = 3.605551275 + 3.5 Combine like terms: 3.605551275 + 3.5 = 7.105551275 m = 7.105551275 Simplifying m = 7.105551275Subproblem 2
m + -3.5 = -3.605551275 Simplifying m + -3.5 = -3.605551275 Reorder the terms: -3.5 + m = -3.605551275 Solving -3.5 + m = -3.605551275 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + m = -3.605551275 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + m = -3.605551275 + 3.5 m = -3.605551275 + 3.5 Combine like terms: -3.605551275 + 3.5 = -0.105551275 m = -0.105551275 Simplifying m = -0.105551275Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.105551275, -0.105551275}
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