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Simplifying 8m2 + -16m + -60 = 0 Reorder the terms: -60 + -16m + 8m2 = 0 Solving -60 + -16m + 8m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -4m + 2m2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + -4m + 2m2)' equal to zero and attempt to solve: Simplifying -15 + -4m + 2m2 = 0 Solving -15 + -4m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -2m + m2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -2m + 7.5 + m2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -2m + m2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -2m + m2 = 0 + 7.5 -2m + m2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -2m + m2 = 7.5 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = 7.5 + 1 Reorder the terms: 1 + -2m + m2 = 7.5 + 1 Combine like terms: 7.5 + 1 = 8.5 1 + -2m + m2 = 8.5 Factor a perfect square on the left side: (m + -1)(m + -1) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (m + -1) equal to 2.915475947 and -2.915475947.Subproblem 1
m + -1 = 2.915475947 Simplifying m + -1 = 2.915475947 Reorder the terms: -1 + m = 2.915475947 Solving -1 + m = 2.915475947 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 2.915475947 + 1 Combine like terms: -1 + 1 = 0 0 + m = 2.915475947 + 1 m = 2.915475947 + 1 Combine like terms: 2.915475947 + 1 = 3.915475947 m = 3.915475947 Simplifying m = 3.915475947Subproblem 2
m + -1 = -2.915475947 Simplifying m + -1 = -2.915475947 Reorder the terms: -1 + m = -2.915475947 Solving -1 + m = -2.915475947 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -2.915475947 + 1 Combine like terms: -1 + 1 = 0 0 + m = -2.915475947 + 1 m = -2.915475947 + 1 Combine like terms: -2.915475947 + 1 = -1.915475947 m = -1.915475947 Simplifying m = -1.915475947Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.915475947, -1.915475947}Solution
m = {3.915475947, -1.915475947}
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