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Simplifying 15t * 15t + -15t + 30 = 0 Reorder the terms for easier multiplication: 15 * 15t * t + -15t + 30 = 0 Multiply 15 * 15 225t * t + -15t + 30 = 0 Multiply t * t 225t2 + -15t + 30 = 0 Reorder the terms: 30 + -15t + 225t2 = 0 Solving 30 + -15t + 225t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '15'. 15(2 + -1t + 15t2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(2 + -1t + 15t2)' equal to zero and attempt to solve: Simplifying 2 + -1t + 15t2 = 0 Solving 2 + -1t + 15t2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.1333333333 + -0.06666666667t + t2 = 0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + -0.06666666667t + -0.1333333333 + t2 = 0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + -0.06666666667t + t2 = 0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + -0.06666666667t + t2 = 0 + -0.1333333333 -0.06666666667t + t2 = 0 + -0.1333333333 Combine like terms: 0 + -0.1333333333 = -0.1333333333 -0.06666666667t + t2 = -0.1333333333 The t term is -0.06666666667t. Take half its coefficient (-0.03333333334). Square it (0.001111111112) and add it to both sides. Add '0.001111111112' to each side of the equation. -0.06666666667t + 0.001111111112 + t2 = -0.1333333333 + 0.001111111112 Reorder the terms: 0.001111111112 + -0.06666666667t + t2 = -0.1333333333 + 0.001111111112 Combine like terms: -0.1333333333 + 0.001111111112 = -0.132222222188 0.001111111112 + -0.06666666667t + t2 = -0.132222222188 Factor a perfect square on the left side: (t + -0.03333333334)(t + -0.03333333334) = -0.132222222188 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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