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Simplifying -4.9t2 + 179t + 12.4 = 0 Reorder the terms: 12.4 + 179t + -4.9t2 = 0 Solving 12.4 + 179t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -2.530612245 + -36.53061224t + t2 = 0 Move the constant term to the right: Add '2.530612245' to each side of the equation. -2.530612245 + -36.53061224t + 2.530612245 + t2 = 0 + 2.530612245 Reorder the terms: -2.530612245 + 2.530612245 + -36.53061224t + t2 = 0 + 2.530612245 Combine like terms: -2.530612245 + 2.530612245 = 0.000000000 0.000000000 + -36.53061224t + t2 = 0 + 2.530612245 -36.53061224t + t2 = 0 + 2.530612245 Combine like terms: 0 + 2.530612245 = 2.530612245 -36.53061224t + t2 = 2.530612245 The t term is -36.53061224t. Take half its coefficient (-18.26530612). Square it (333.6214077) and add it to both sides. Add '333.6214077' to each side of the equation. -36.53061224t + 333.6214077 + t2 = 2.530612245 + 333.6214077 Reorder the terms: 333.6214077 + -36.53061224t + t2 = 2.530612245 + 333.6214077 Combine like terms: 2.530612245 + 333.6214077 = 336.152019945 333.6214077 + -36.53061224t + t2 = 336.152019945 Factor a perfect square on the left side: (t + -18.26530612)(t + -18.26530612) = 336.152019945 Calculate the square root of the right side: 18.334448995 Break this problem into two subproblems by setting (t + -18.26530612) equal to 18.334448995 and -18.334448995.Subproblem 1
t + -18.26530612 = 18.334448995 Simplifying t + -18.26530612 = 18.334448995 Reorder the terms: -18.26530612 + t = 18.334448995 Solving -18.26530612 + t = 18.334448995 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18.26530612' to each side of the equation. -18.26530612 + 18.26530612 + t = 18.334448995 + 18.26530612 Combine like terms: -18.26530612 + 18.26530612 = 0.00000000 0.00000000 + t = 18.334448995 + 18.26530612 t = 18.334448995 + 18.26530612 Combine like terms: 18.334448995 + 18.26530612 = 36.599755115 t = 36.599755115 Simplifying t = 36.599755115Subproblem 2
t + -18.26530612 = -18.334448995 Simplifying t + -18.26530612 = -18.334448995 Reorder the terms: -18.26530612 + t = -18.334448995 Solving -18.26530612 + t = -18.334448995 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18.26530612' to each side of the equation. -18.26530612 + 18.26530612 + t = -18.334448995 + 18.26530612 Combine like terms: -18.26530612 + 18.26530612 = 0.00000000 0.00000000 + t = -18.334448995 + 18.26530612 t = -18.334448995 + 18.26530612 Combine like terms: -18.334448995 + 18.26530612 = -0.069142875 t = -0.069142875 Simplifying t = -0.069142875Solution
The solution to the problem is based on the solutions from the subproblems. t = {36.599755115, -0.069142875}
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