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Simplifying 84m2 + -22m + -42 = 0 Reorder the terms: -42 + -22m + 84m2 = 0 Solving -42 + -22m + 84m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -11m + 42m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -11m + 42m2)' equal to zero and attempt to solve: Simplifying -21 + -11m + 42m2 = 0 Solving -21 + -11m + 42m2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -0.5 + -0.2619047619m + m2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.2619047619m + 0.5 + m2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.2619047619m + m2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.2619047619m + m2 = 0 + 0.5 -0.2619047619m + m2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.2619047619m + m2 = 0.5 The m term is -0.2619047619m. Take half its coefficient (-0.130952381). Square it (0.01714852609) and add it to both sides. Add '0.01714852609' to each side of the equation. -0.2619047619m + 0.01714852609 + m2 = 0.5 + 0.01714852609 Reorder the terms: 0.01714852609 + -0.2619047619m + m2 = 0.5 + 0.01714852609 Combine like terms: 0.5 + 0.01714852609 = 0.51714852609 0.01714852609 + -0.2619047619m + m2 = 0.51714852609 Factor a perfect square on the left side: (m + -0.130952381)(m + -0.130952381) = 0.51714852609 Calculate the square root of the right side: 0.719130396 Break this problem into two subproblems by setting (m + -0.130952381) equal to 0.719130396 and -0.719130396.Subproblem 1
m + -0.130952381 = 0.719130396 Simplifying m + -0.130952381 = 0.719130396 Reorder the terms: -0.130952381 + m = 0.719130396 Solving -0.130952381 + m = 0.719130396 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.130952381' to each side of the equation. -0.130952381 + 0.130952381 + m = 0.719130396 + 0.130952381 Combine like terms: -0.130952381 + 0.130952381 = 0.000000000 0.000000000 + m = 0.719130396 + 0.130952381 m = 0.719130396 + 0.130952381 Combine like terms: 0.719130396 + 0.130952381 = 0.850082777 m = 0.850082777 Simplifying m = 0.850082777Subproblem 2
m + -0.130952381 = -0.719130396 Simplifying m + -0.130952381 = -0.719130396 Reorder the terms: -0.130952381 + m = -0.719130396 Solving -0.130952381 + m = -0.719130396 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.130952381' to each side of the equation. -0.130952381 + 0.130952381 + m = -0.719130396 + 0.130952381 Combine like terms: -0.130952381 + 0.130952381 = 0.000000000 0.000000000 + m = -0.719130396 + 0.130952381 m = -0.719130396 + 0.130952381 Combine like terms: -0.719130396 + 0.130952381 = -0.588178015 m = -0.588178015 Simplifying m = -0.588178015Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.850082777, -0.588178015}Solution
m = {0.850082777, -0.588178015}
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