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Simplifying -5t2 + 3t + 80 = 0 Reorder the terms: 80 + 3t + -5t2 = 0 Solving 80 + 3t + -5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -16 + -0.6t + t2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -0.6t + 16 + t2 = 0 + 16 Reorder the terms: -16 + 16 + -0.6t + t2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -0.6t + t2 = 0 + 16 -0.6t + t2 = 0 + 16 Combine like terms: 0 + 16 = 16 -0.6t + t2 = 16 The t term is -0.6t. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6t + 0.09 + t2 = 16 + 0.09 Reorder the terms: 0.09 + -0.6t + t2 = 16 + 0.09 Combine like terms: 16 + 0.09 = 16.09 0.09 + -0.6t + t2 = 16.09 Factor a perfect square on the left side: (t + -0.3)(t + -0.3) = 16.09 Calculate the square root of the right side: 4.011234224 Break this problem into two subproblems by setting (t + -0.3) equal to 4.011234224 and -4.011234224.Subproblem 1
t + -0.3 = 4.011234224 Simplifying t + -0.3 = 4.011234224 Reorder the terms: -0.3 + t = 4.011234224 Solving -0.3 + t = 4.011234224 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + t = 4.011234224 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + t = 4.011234224 + 0.3 t = 4.011234224 + 0.3 Combine like terms: 4.011234224 + 0.3 = 4.311234224 t = 4.311234224 Simplifying t = 4.311234224Subproblem 2
t + -0.3 = -4.011234224 Simplifying t + -0.3 = -4.011234224 Reorder the terms: -0.3 + t = -4.011234224 Solving -0.3 + t = -4.011234224 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + t = -4.011234224 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + t = -4.011234224 + 0.3 t = -4.011234224 + 0.3 Combine like terms: -4.011234224 + 0.3 = -3.711234224 t = -3.711234224 Simplifying t = -3.711234224Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.311234224, -3.711234224}
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