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Simplifying -2m2 + 56m + 90 = 0 Reorder the terms: 90 + 56m + -2m2 = 0 Solving 90 + 56m + -2m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(45 + 28m + -1m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(45 + 28m + -1m2)' equal to zero and attempt to solve: Simplifying 45 + 28m + -1m2 = 0 Solving 45 + 28m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -45 + -28m + m2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + -28m + 45 + m2 = 0 + 45 Reorder the terms: -45 + 45 + -28m + m2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -28m + m2 = 0 + 45 -28m + m2 = 0 + 45 Combine like terms: 0 + 45 = 45 -28m + m2 = 45 The m term is -28m. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28m + 196 + m2 = 45 + 196 Reorder the terms: 196 + -28m + m2 = 45 + 196 Combine like terms: 45 + 196 = 241 196 + -28m + m2 = 241 Factor a perfect square on the left side: (m + -14)(m + -14) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (m + -14) equal to 15.524174696 and -15.524174696.Subproblem 1
m + -14 = 15.524174696 Simplifying m + -14 = 15.524174696 Reorder the terms: -14 + m = 15.524174696 Solving -14 + m = 15.524174696 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + m = 15.524174696 + 14 Combine like terms: -14 + 14 = 0 0 + m = 15.524174696 + 14 m = 15.524174696 + 14 Combine like terms: 15.524174696 + 14 = 29.524174696 m = 29.524174696 Simplifying m = 29.524174696Subproblem 2
m + -14 = -15.524174696 Simplifying m + -14 = -15.524174696 Reorder the terms: -14 + m = -15.524174696 Solving -14 + m = -15.524174696 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + m = -15.524174696 + 14 Combine like terms: -14 + 14 = 0 0 + m = -15.524174696 + 14 m = -15.524174696 + 14 Combine like terms: -15.524174696 + 14 = -1.524174696 m = -1.524174696 Simplifying m = -1.524174696Solution
The solution to the problem is based on the solutions from the subproblems. m = {29.524174696, -1.524174696}Solution
m = {29.524174696, -1.524174696}
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