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Simplifying 6m4 + 9 = 24m2 Reorder the terms: 9 + 6m4 = 24m2 Solving 9 + 6m4 = 24m2 Solving for variable 'm'. Reorder the terms: 9 + -24m2 + 6m4 = 24m2 + -24m2 Combine like terms: 24m2 + -24m2 = 0 9 + -24m2 + 6m4 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -8m2 + 2m4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -8m2 + 2m4)' equal to zero and attempt to solve: Simplifying 3 + -8m2 + 2m4 = 0 Solving 3 + -8m2 + 2m4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -4m2 + m4 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -4m2 + -1.5 + m4 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -4m2 + m4 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -4m2 + m4 = 0 + -1.5 -4m2 + m4 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -4m2 + m4 = -1.5 The m term is -4m2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m2 + 4 + m4 = -1.5 + 4 Reorder the terms: 4 + -4m2 + m4 = -1.5 + 4 Combine like terms: -1.5 + 4 = 2.5 4 + -4m2 + m4 = 2.5 Factor a perfect square on the left side: (m2 + -2)(m2 + -2) = 2.5 Calculate the square root of the right side: 1.58113883 Break this problem into two subproblems by setting (m2 + -2) equal to 1.58113883 and -1.58113883.Subproblem 1
m2 + -2 = 1.58113883 Simplifying m2 + -2 = 1.58113883 Reorder the terms: -2 + m2 = 1.58113883 Solving -2 + m2 = 1.58113883 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m2 = 1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + m2 = 1.58113883 + 2 m2 = 1.58113883 + 2 Combine like terms: 1.58113883 + 2 = 3.58113883 m2 = 3.58113883 Simplifying m2 = 3.58113883 Take the square root of each side: m = {-1.892389714, 1.892389714}Subproblem 2
m2 + -2 = -1.58113883 Simplifying m2 + -2 = -1.58113883 Reorder the terms: -2 + m2 = -1.58113883 Solving -2 + m2 = -1.58113883 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m2 = -1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + m2 = -1.58113883 + 2 m2 = -1.58113883 + 2 Combine like terms: -1.58113883 + 2 = 0.41886117 m2 = 0.41886117 Simplifying m2 = 0.41886117 Take the square root of each side: m = {-0.647194847, 0.647194847}Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.892389714, 1.892389714, -0.647194847, 0.647194847}Solution
m = {-1.892389714, 1.892389714, -0.647194847, 0.647194847}
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