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Simplifying 8(3m + 5) * 2m = -4 Reorder the terms: 8(5 + 3m) * 2m = -4 Reorder the terms for easier multiplication: 8 * 2m(5 + 3m) = -4 Multiply 8 * 2 16m(5 + 3m) = -4 (5 * 16m + 3m * 16m) = -4 (80m + 48m2) = -4 Solving 80m + 48m2 = -4 Solving for variable 'm'. Reorder the terms: 4 + 80m + 48m2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + 80m + 48m2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 20m + 12m2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 20m + 12m2)' equal to zero and attempt to solve: Simplifying 1 + 20m + 12m2 = 0 Solving 1 + 20m + 12m2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.08333333333 + 1.666666667m + m2 = 0 Move the constant term to the right: Add '-0.08333333333' to each side of the equation. 0.08333333333 + 1.666666667m + -0.08333333333 + m2 = 0 + -0.08333333333 Reorder the terms: 0.08333333333 + -0.08333333333 + 1.666666667m + m2 = 0 + -0.08333333333 Combine like terms: 0.08333333333 + -0.08333333333 = 0.00000000000 0.00000000000 + 1.666666667m + m2 = 0 + -0.08333333333 1.666666667m + m2 = 0 + -0.08333333333 Combine like terms: 0 + -0.08333333333 = -0.08333333333 1.666666667m + m2 = -0.08333333333 The m term is 1.666666667m. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667m + 0.6944444447 + m2 = -0.08333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667m + m2 = -0.08333333333 + 0.6944444447 Combine like terms: -0.08333333333 + 0.6944444447 = 0.61111111137 0.6944444447 + 1.666666667m + m2 = 0.61111111137 Factor a perfect square on the left side: (m + 0.8333333335)(m + 0.8333333335) = 0.61111111137 Calculate the square root of the right side: 0.78173596 Break this problem into two subproblems by setting (m + 0.8333333335) equal to 0.78173596 and -0.78173596.Subproblem 1
m + 0.8333333335 = 0.78173596 Simplifying m + 0.8333333335 = 0.78173596 Reorder the terms: 0.8333333335 + m = 0.78173596 Solving 0.8333333335 + m = 0.78173596 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + m = 0.78173596 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + m = 0.78173596 + -0.8333333335 m = 0.78173596 + -0.8333333335 Combine like terms: 0.78173596 + -0.8333333335 = -0.0515973735 m = -0.0515973735 Simplifying m = -0.0515973735Subproblem 2
m + 0.8333333335 = -0.78173596 Simplifying m + 0.8333333335 = -0.78173596 Reorder the terms: 0.8333333335 + m = -0.78173596 Solving 0.8333333335 + m = -0.78173596 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + m = -0.78173596 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + m = -0.78173596 + -0.8333333335 m = -0.78173596 + -0.8333333335 Combine like terms: -0.78173596 + -0.8333333335 = -1.6150692935 m = -1.6150692935 Simplifying m = -1.6150692935Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.0515973735, -1.6150692935}Solution
m = {-0.0515973735, -1.6150692935}
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