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Simplifying -4.9t2 + 18t + 1.3 = 0 Reorder the terms: 1.3 + 18t + -4.9t2 = 0 Solving 1.3 + 18t + -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'. -0.2653061224 + -3.673469388t + t2 = 0 Move the constant term to the right: Add '0.2653061224' to each side of the equation. -0.2653061224 + -3.673469388t + 0.2653061224 + t2 = 0 + 0.2653061224 Reorder the terms: -0.2653061224 + 0.2653061224 + -3.673469388t + t2 = 0 + 0.2653061224 Combine like terms: -0.2653061224 + 0.2653061224 = 0.0000000000 0.0000000000 + -3.673469388t + t2 = 0 + 0.2653061224 -3.673469388t + t2 = 0 + 0.2653061224 Combine like terms: 0 + 0.2653061224 = 0.2653061224 -3.673469388t + t2 = 0.2653061224 The t term is -3.673469388t. Take half its coefficient (-1.836734694). Square it (3.373594336) and add it to both sides. Add '3.373594336' to each side of the equation. -3.673469388t + 3.373594336 + t2 = 0.2653061224 + 3.373594336 Reorder the terms: 3.373594336 + -3.673469388t + t2 = 0.2653061224 + 3.373594336 Combine like terms: 0.2653061224 + 3.373594336 = 3.6389004584 3.373594336 + -3.673469388t + t2 = 3.6389004584 Factor a perfect square on the left side: (t + -1.836734694)(t + -1.836734694) = 3.6389004584 Calculate the square root of the right side: 1.907590223 Break this problem into two subproblems by setting (t + -1.836734694) equal to 1.907590223 and -1.907590223.Subproblem 1
t + -1.836734694 = 1.907590223 Simplifying t + -1.836734694 = 1.907590223 Reorder the terms: -1.836734694 + t = 1.907590223 Solving -1.836734694 + t = 1.907590223 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.836734694' to each side of the equation. -1.836734694 + 1.836734694 + t = 1.907590223 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = 1.907590223 + 1.836734694 t = 1.907590223 + 1.836734694 Combine like terms: 1.907590223 + 1.836734694 = 3.744324917 t = 3.744324917 Simplifying t = 3.744324917Subproblem 2
t + -1.836734694 = -1.907590223 Simplifying t + -1.836734694 = -1.907590223 Reorder the terms: -1.836734694 + t = -1.907590223 Solving -1.836734694 + t = -1.907590223 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.836734694' to each side of the equation. -1.836734694 + 1.836734694 + t = -1.907590223 + 1.836734694 Combine like terms: -1.836734694 + 1.836734694 = 0.000000000 0.000000000 + t = -1.907590223 + 1.836734694 t = -1.907590223 + 1.836734694 Combine like terms: -1.907590223 + 1.836734694 = -0.070855529 t = -0.070855529 Simplifying t = -0.070855529Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.744324917, -0.070855529}
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