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Simplifying -4.9t2 + 10t + 1.5 = 0 Reorder the terms: 1.5 + 10t + -4.9t2 = 0 Solving 1.5 + 10t + -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'. -0.306122449 + -2.040816327t + t2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -2.040816327t + 0.306122449 + t2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -2.040816327t + t2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -2.040816327t + t2 = 0 + 0.306122449 -2.040816327t + t2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -2.040816327t + t2 = 0.306122449 The t term is -2.040816327t. Take half its coefficient (-1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. -2.040816327t + 1.041232821 + t2 = 0.306122449 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327t + t2 = 0.306122449 + 1.041232821 Combine like terms: 0.306122449 + 1.041232821 = 1.34735527 1.041232821 + -2.040816327t + t2 = 1.34735527 Factor a perfect square on the left side: (t + -1.020408164)(t + -1.020408164) = 1.34735527 Calculate the square root of the right side: 1.160756335 Break this problem into two subproblems by setting (t + -1.020408164) equal to 1.160756335 and -1.160756335.Subproblem 1
t + -1.020408164 = 1.160756335 Simplifying t + -1.020408164 = 1.160756335 Reorder the terms: -1.020408164 + t = 1.160756335 Solving -1.020408164 + t = 1.160756335 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = 1.160756335 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = 1.160756335 + 1.020408164 t = 1.160756335 + 1.020408164 Combine like terms: 1.160756335 + 1.020408164 = 2.181164499 t = 2.181164499 Simplifying t = 2.181164499Subproblem 2
t + -1.020408164 = -1.160756335 Simplifying t + -1.020408164 = -1.160756335 Reorder the terms: -1.020408164 + t = -1.160756335 Solving -1.020408164 + t = -1.160756335 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + t = -1.160756335 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + t = -1.160756335 + 1.020408164 t = -1.160756335 + 1.020408164 Combine like terms: -1.160756335 + 1.020408164 = -0.140348171 t = -0.140348171 Simplifying t = -0.140348171Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.181164499, -0.140348171}
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