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Simplifying 12m2 + -21 = -3m Reorder the terms: -21 + 12m2 = -3m Solving -21 + 12m2 = -3m Solving for variable 'm'. Reorder the terms: -21 + 3m + 12m2 = -3m + 3m Combine like terms: -3m + 3m = 0 -21 + 3m + 12m2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + m + 4m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + m + 4m2)' equal to zero and attempt to solve: Simplifying -7 + m + 4m2 = 0 Solving -7 + m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 0.25m + m2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 0.25m + 1.75 + m2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 0.25m + m2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 0.25m + m2 = 0 + 1.75 0.25m + m2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 0.25m + m2 = 1.75 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25m + 0.25 + m2 = 1.75 + 0.25 Reorder the terms: 0.25 + 0.25m + m2 = 1.75 + 0.25 Combine like terms: 1.75 + 0.25 = 2 0.25 + 0.25m + m2 = 2 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (m + 0.5) equal to 1.414213562 and -1.414213562.Subproblem 1
m + 0.5 = 1.414213562 Simplifying m + 0.5 = 1.414213562 Reorder the terms: 0.5 + m = 1.414213562 Solving 0.5 + m = 1.414213562 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 1.414213562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 1.414213562 + -0.5 m = 1.414213562 + -0.5 Combine like terms: 1.414213562 + -0.5 = 0.914213562 m = 0.914213562 Simplifying m = 0.914213562Subproblem 2
m + 0.5 = -1.414213562 Simplifying m + 0.5 = -1.414213562 Reorder the terms: 0.5 + m = -1.414213562 Solving 0.5 + m = -1.414213562 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -1.414213562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -1.414213562 + -0.5 m = -1.414213562 + -0.5 Combine like terms: -1.414213562 + -0.5 = -1.914213562 m = -1.914213562 Simplifying m = -1.914213562Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.914213562, -1.914213562}Solution
m = {0.914213562, -1.914213562}
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