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Simplifying 5t8(t + -1t2 + 6t3) = 0 (t * 5t8 + -1t2 * 5t8 + 6t3 * 5t8) = 0 (5t9 + -5t10 + 30t11) = 0 Solving 5t9 + -5t10 + 30t11 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5t9'. 5t9(1 + -1t + 6t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 't9' equal to zero and attempt to solve: Simplifying t9 = 0 Solving t9 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t9 = 0 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 '(1 + -1t + 6t2)' equal to zero and attempt to solve: Simplifying 1 + -1t + 6t2 = 0 Solving 1 + -1t + 6t2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + -0.1666666667t + t2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667t + -0.1666666667 + t2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -0.1666666667t + t2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -0.1666666667t + t2 = 0 + -0.1666666667 -0.1666666667t + t2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -0.1666666667t + t2 = -0.1666666667 The t term is -0.1666666667t. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667t + 0.006944444447 + t2 = -0.1666666667 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667t + t2 = -0.1666666667 + 0.006944444447 Combine like terms: -0.1666666667 + 0.006944444447 = -0.159722222253 0.006944444447 + -0.1666666667t + t2 = -0.159722222253 Factor a perfect square on the left side: (t + -0.08333333335)(t + -0.08333333335) = -0.159722222253 Can't calculate square root of the right side. 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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