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Simplifying 4.9t2 + -2.9958t + -0.78 = 0 Reorder the terms: -0.78 + -2.9958t + 4.9t2 = 0 Solving -0.78 + -2.9958t + 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'. -0.1591836735 + -0.6113877551t + t2 = 0 Move the constant term to the right: Add '0.1591836735' to each side of the equation. -0.1591836735 + -0.6113877551t + 0.1591836735 + t2 = 0 + 0.1591836735 Reorder the terms: -0.1591836735 + 0.1591836735 + -0.6113877551t + t2 = 0 + 0.1591836735 Combine like terms: -0.1591836735 + 0.1591836735 = 0.0000000000 0.0000000000 + -0.6113877551t + t2 = 0 + 0.1591836735 -0.6113877551t + t2 = 0 + 0.1591836735 Combine like terms: 0 + 0.1591836735 = 0.1591836735 -0.6113877551t + t2 = 0.1591836735 The t term is -0.6113877551t. Take half its coefficient (-0.3056938776). Square it (0.09344874680) and add it to both sides. Add '0.09344874680' to each side of the equation. -0.6113877551t + 0.09344874680 + t2 = 0.1591836735 + 0.09344874680 Reorder the terms: 0.09344874680 + -0.6113877551t + t2 = 0.1591836735 + 0.09344874680 Combine like terms: 0.1591836735 + 0.09344874680 = 0.2526324203 0.09344874680 + -0.6113877551t + t2 = 0.2526324203 Factor a perfect square on the left side: (t + -0.3056938776)(t + -0.3056938776) = 0.2526324203 Calculate the square root of the right side: 0.502625527 Break this problem into two subproblems by setting (t + -0.3056938776) equal to 0.502625527 and -0.502625527.Subproblem 1
t + -0.3056938776 = 0.502625527 Simplifying t + -0.3056938776 = 0.502625527 Reorder the terms: -0.3056938776 + t = 0.502625527 Solving -0.3056938776 + t = 0.502625527 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3056938776' to each side of the equation. -0.3056938776 + 0.3056938776 + t = 0.502625527 + 0.3056938776 Combine like terms: -0.3056938776 + 0.3056938776 = 0.0000000000 0.0000000000 + t = 0.502625527 + 0.3056938776 t = 0.502625527 + 0.3056938776 Combine like terms: 0.502625527 + 0.3056938776 = 0.8083194046 t = 0.8083194046 Simplifying t = 0.8083194046Subproblem 2
t + -0.3056938776 = -0.502625527 Simplifying t + -0.3056938776 = -0.502625527 Reorder the terms: -0.3056938776 + t = -0.502625527 Solving -0.3056938776 + t = -0.502625527 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3056938776' to each side of the equation. -0.3056938776 + 0.3056938776 + t = -0.502625527 + 0.3056938776 Combine like terms: -0.3056938776 + 0.3056938776 = 0.0000000000 0.0000000000 + t = -0.502625527 + 0.3056938776 t = -0.502625527 + 0.3056938776 Combine like terms: -0.502625527 + 0.3056938776 = -0.1969316494 t = -0.1969316494 Simplifying t = -0.1969316494Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.8083194046, -0.1969316494}
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