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Simplifying 30t2 + -9t + -63 = 0 Reorder the terms: -63 + -9t + 30t2 = 0 Solving -63 + -9t + 30t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + -3t + 10t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-21 + -3t + 10t2)' equal to zero and attempt to solve: Simplifying -21 + -3t + 10t2 = 0 Solving -21 + -3t + 10t2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.1 + -0.3t + t2 = 0.0 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + -0.3t + 2.1 + t2 = 0.0 + 2.1 Reorder the terms: -2.1 + 2.1 + -0.3t + t2 = 0.0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + -0.3t + t2 = 0.0 + 2.1 -0.3t + t2 = 0.0 + 2.1 Combine like terms: 0.0 + 2.1 = 2.1 -0.3t + t2 = 2.1 The t term is -0.3t. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3t + 0.0225 + t2 = 2.1 + 0.0225 Reorder the terms: 0.0225 + -0.3t + t2 = 2.1 + 0.0225 Combine like terms: 2.1 + 0.0225 = 2.1225 0.0225 + -0.3t + t2 = 2.1225 Factor a perfect square on the left side: (t + -0.15)(t + -0.15) = 2.1225 Calculate the square root of the right side: 1.456880228 Break this problem into two subproblems by setting (t + -0.15) equal to 1.456880228 and -1.456880228.Subproblem 1
t + -0.15 = 1.456880228 Simplifying t + -0.15 = 1.456880228 Reorder the terms: -0.15 + t = 1.456880228 Solving -0.15 + t = 1.456880228 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + t = 1.456880228 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + t = 1.456880228 + 0.15 t = 1.456880228 + 0.15 Combine like terms: 1.456880228 + 0.15 = 1.606880228 t = 1.606880228 Simplifying t = 1.606880228Subproblem 2
t + -0.15 = -1.456880228 Simplifying t + -0.15 = -1.456880228 Reorder the terms: -0.15 + t = -1.456880228 Solving -0.15 + t = -1.456880228 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + t = -1.456880228 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + t = -1.456880228 + 0.15 t = -1.456880228 + 0.15 Combine like terms: -1.456880228 + 0.15 = -1.306880228 t = -1.306880228 Simplifying t = -1.306880228Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.606880228, -1.306880228}Solution
t = {1.606880228, -1.306880228}
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