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Simplifying 12t2 + -20t + -150 = 0 Reorder the terms: -150 + -20t + 12t2 = 0 Solving -150 + -20t + 12t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-75 + -10t + 6t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-75 + -10t + 6t2)' equal to zero and attempt to solve: Simplifying -75 + -10t + 6t2 = 0 Solving -75 + -10t + 6t2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -12.5 + -1.666666667t + t2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -1.666666667t + 12.5 + t2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -1.666666667t + t2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -1.666666667t + t2 = 0 + 12.5 -1.666666667t + t2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -1.666666667t + t2 = 12.5 The t term is -1.666666667t. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667t + 0.6944444447 + t2 = 12.5 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667t + t2 = 12.5 + 0.6944444447 Combine like terms: 12.5 + 0.6944444447 = 13.1944444447 0.6944444447 + -1.666666667t + t2 = 13.1944444447 Factor a perfect square on the left side: (t + -0.8333333335)(t + -0.8333333335) = 13.1944444447 Calculate the square root of the right side: 3.632415786 Break this problem into two subproblems by setting (t + -0.8333333335) equal to 3.632415786 and -3.632415786.Subproblem 1
t + -0.8333333335 = 3.632415786 Simplifying t + -0.8333333335 = 3.632415786 Reorder the terms: -0.8333333335 + t = 3.632415786 Solving -0.8333333335 + t = 3.632415786 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + t = 3.632415786 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + t = 3.632415786 + 0.8333333335 t = 3.632415786 + 0.8333333335 Combine like terms: 3.632415786 + 0.8333333335 = 4.4657491195 t = 4.4657491195 Simplifying t = 4.4657491195Subproblem 2
t + -0.8333333335 = -3.632415786 Simplifying t + -0.8333333335 = -3.632415786 Reorder the terms: -0.8333333335 + t = -3.632415786 Solving -0.8333333335 + t = -3.632415786 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + t = -3.632415786 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + t = -3.632415786 + 0.8333333335 t = -3.632415786 + 0.8333333335 Combine like terms: -3.632415786 + 0.8333333335 = -2.7990824525 t = -2.7990824525 Simplifying t = -2.7990824525Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.4657491195, -2.7990824525}Solution
t = {4.4657491195, -2.7990824525}
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