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Simplifying 64m4 + -58m2 + -16 = 0 Reorder the terms: -16 + -58m2 + 64m4 = 0 Solving -16 + -58m2 + 64m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -29m2 + 32m4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -29m2 + 32m4)' equal to zero and attempt to solve: Simplifying -8 + -29m2 + 32m4 = 0 Solving -8 + -29m2 + 32m4 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.25 + -0.90625m2 + m4 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.90625m2 + 0.25 + m4 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.90625m2 + m4 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.90625m2 + m4 = 0 + 0.25 -0.90625m2 + m4 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.90625m2 + m4 = 0.25 The m term is -0.90625m2. Take half its coefficient (-0.453125). Square it (0.2053222656) and add it to both sides. Add '0.2053222656' to each side of the equation. -0.90625m2 + 0.2053222656 + m4 = 0.25 + 0.2053222656 Reorder the terms: 0.2053222656 + -0.90625m2 + m4 = 0.25 + 0.2053222656 Combine like terms: 0.25 + 0.2053222656 = 0.4553222656 0.2053222656 + -0.90625m2 + m4 = 0.4553222656 Factor a perfect square on the left side: (m2 + -0.453125)(m2 + -0.453125) = 0.4553222656 Calculate the square root of the right side: 0.674775715 Break this problem into two subproblems by setting (m2 + -0.453125) equal to 0.674775715 and -0.674775715.Subproblem 1
m2 + -0.453125 = 0.674775715 Simplifying m2 + -0.453125 = 0.674775715 Reorder the terms: -0.453125 + m2 = 0.674775715 Solving -0.453125 + m2 = 0.674775715 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.453125' to each side of the equation. -0.453125 + 0.453125 + m2 = 0.674775715 + 0.453125 Combine like terms: -0.453125 + 0.453125 = 0.000000 0.000000 + m2 = 0.674775715 + 0.453125 m2 = 0.674775715 + 0.453125 Combine like terms: 0.674775715 + 0.453125 = 1.127900715 m2 = 1.127900715 Simplifying m2 = 1.127900715 Take the square root of each side: m = {-1.062026702, 1.062026702}Subproblem 2
m2 + -0.453125 = -0.674775715 Simplifying m2 + -0.453125 = -0.674775715 Reorder the terms: -0.453125 + m2 = -0.674775715 Solving -0.453125 + m2 = -0.674775715 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.453125' to each side of the equation. -0.453125 + 0.453125 + m2 = -0.674775715 + 0.453125 Combine like terms: -0.453125 + 0.453125 = 0.000000 0.000000 + m2 = -0.674775715 + 0.453125 m2 = -0.674775715 + 0.453125 Combine like terms: -0.674775715 + 0.453125 = -0.221650715 m2 = -0.221650715 Simplifying m2 = -0.221650715 Reorder the terms: 0.221650715 + m2 = -0.221650715 + 0.221650715 Combine like terms: -0.221650715 + 0.221650715 = 0.000000000 0.221650715 + 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. 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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