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Simplifying -24m2q + -3mq + 15q = 0 Reorder the terms: -3mq + -24m2q + 15q = 0 Solving -3mq + -24m2q + 15q = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3q'. 3q(-1m + -8m2 + 5) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'q' equal to zero and attempt to solve: Simplifying q = 0 Solving q = 0 Move all terms containing m to the left, all other terms to the right. Add '-1q' to each side of the equation. q + -1q = 0 + -1q Remove the zero: 0 = -1q Simplifying 0 = -1q The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1m + -8m2 + 5)' equal to zero and attempt to solve: Simplifying -1m + -8m2 + 5 = 0 Reorder the terms: 5 + -1m + -8m2 = 0 Solving 5 + -1m + -8m2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + 0.125m + m2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.125m + 0.625 + m2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.125m + m2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.125m + m2 = 0 + 0.625 0.125m + m2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.125m + m2 = 0.625 The m term is 0.125m. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125m + 0.00390625 + m2 = 0.625 + 0.00390625 Reorder the terms: 0.00390625 + 0.125m + m2 = 0.625 + 0.00390625 Combine like terms: 0.625 + 0.00390625 = 0.62890625 0.00390625 + 0.125m + m2 = 0.62890625 Factor a perfect square on the left side: (m + 0.0625)(m + 0.0625) = 0.62890625 Calculate the square root of the right side: 0.793036096 Break this problem into two subproblems by setting (m + 0.0625) equal to 0.793036096 and -0.793036096.Subproblem 1
m + 0.0625 = 0.793036096 Simplifying m + 0.0625 = 0.793036096 Reorder the terms: 0.0625 + m = 0.793036096 Solving 0.0625 + m = 0.793036096 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + m = 0.793036096 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + m = 0.793036096 + -0.0625 m = 0.793036096 + -0.0625 Combine like terms: 0.793036096 + -0.0625 = 0.730536096 m = 0.730536096 Simplifying m = 0.730536096Subproblem 2
m + 0.0625 = -0.793036096 Simplifying m + 0.0625 = -0.793036096 Reorder the terms: 0.0625 + m = -0.793036096 Solving 0.0625 + m = -0.793036096 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + m = -0.793036096 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + m = -0.793036096 + -0.0625 m = -0.793036096 + -0.0625 Combine like terms: -0.793036096 + -0.0625 = -0.855536096 m = -0.855536096 Simplifying m = -0.855536096Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.730536096, -0.855536096}Solution
m = {0.730536096, -0.855536096}
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