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Simplifying m4 + -4m2 + -1(2) = 0 Multiply -1 * 2 m4 + -4m2 + -2 = 0 Reorder the terms: -2 + -4m2 + m4 = 0 Solving -2 + -4m2 + m4 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -4m2 + 2 + m4 = 0 + 2 Reorder the terms: -2 + 2 + -4m2 + m4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4m2 + m4 = 0 + 2 -4m2 + m4 = 0 + 2 Combine like terms: 0 + 2 = 2 -4m2 + m4 = 2 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 = 2 + 4 Reorder the terms: 4 + -4m2 + m4 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + -4m2 + m4 = 6 Factor a perfect square on the left side: (m2 + -2)(m2 + -2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (m2 + -2) equal to 2.449489743 and -2.449489743.Subproblem 1
m2 + -2 = 2.449489743 Simplifying m2 + -2 = 2.449489743 Reorder the terms: -2 + m2 = 2.449489743 Solving -2 + m2 = 2.449489743 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 = 2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + m2 = 2.449489743 + 2 m2 = 2.449489743 + 2 Combine like terms: 2.449489743 + 2 = 4.449489743 m2 = 4.449489743 Simplifying m2 = 4.449489743 Take the square root of each side: m = {-2.109381365, 2.109381365}Subproblem 2
m2 + -2 = -2.449489743 Simplifying m2 + -2 = -2.449489743 Reorder the terms: -2 + m2 = -2.449489743 Solving -2 + m2 = -2.449489743 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 = -2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + m2 = -2.449489743 + 2 m2 = -2.449489743 + 2 Combine like terms: -2.449489743 + 2 = -0.449489743 m2 = -0.449489743 Simplifying m2 = -0.449489743 Reorder the terms: 0.449489743 + m2 = -0.449489743 + 0.449489743 Combine like terms: -0.449489743 + 0.449489743 = 0.000000000 0.449489743 + m2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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