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Simplifying 2m2 + -140m + 420 = 0 Reorder the terms: 420 + -140m + 2m2 = 0 Solving 420 + -140m + 2m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(210 + -70m + m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(210 + -70m + m2)' equal to zero and attempt to solve: Simplifying 210 + -70m + m2 = 0 Solving 210 + -70m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-210' to each side of the equation. 210 + -70m + -210 + m2 = 0 + -210 Reorder the terms: 210 + -210 + -70m + m2 = 0 + -210 Combine like terms: 210 + -210 = 0 0 + -70m + m2 = 0 + -210 -70m + m2 = 0 + -210 Combine like terms: 0 + -210 = -210 -70m + m2 = -210 The m term is -70m. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70m + 1225 + m2 = -210 + 1225 Reorder the terms: 1225 + -70m + m2 = -210 + 1225 Combine like terms: -210 + 1225 = 1015 1225 + -70m + m2 = 1015 Factor a perfect square on the left side: (m + -35)(m + -35) = 1015 Calculate the square root of the right side: 31.859064644 Break this problem into two subproblems by setting (m + -35) equal to 31.859064644 and -31.859064644.Subproblem 1
m + -35 = 31.859064644 Simplifying m + -35 = 31.859064644 Reorder the terms: -35 + m = 31.859064644 Solving -35 + m = 31.859064644 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + m = 31.859064644 + 35 Combine like terms: -35 + 35 = 0 0 + m = 31.859064644 + 35 m = 31.859064644 + 35 Combine like terms: 31.859064644 + 35 = 66.859064644 m = 66.859064644 Simplifying m = 66.859064644Subproblem 2
m + -35 = -31.859064644 Simplifying m + -35 = -31.859064644 Reorder the terms: -35 + m = -31.859064644 Solving -35 + m = -31.859064644 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + m = -31.859064644 + 35 Combine like terms: -35 + 35 = 0 0 + m = -31.859064644 + 35 m = -31.859064644 + 35 Combine like terms: -31.859064644 + 35 = 3.140935356 m = 3.140935356 Simplifying m = 3.140935356Solution
The solution to the problem is based on the solutions from the subproblems. m = {66.859064644, 3.140935356}Solution
m = {66.859064644, 3.140935356}
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