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Simplifying 5t2 + -7t + -20 = 0 Reorder the terms: -20 + -7t + 5t2 = 0 Solving -20 + -7t + 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'. -4 + -1.4t + t2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -1.4t + 4 + t2 = 0 + 4 Reorder the terms: -4 + 4 + -1.4t + t2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1.4t + t2 = 0 + 4 -1.4t + t2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1.4t + t2 = 4 The t term is -1.4t. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4t + 0.49 + t2 = 4 + 0.49 Reorder the terms: 0.49 + -1.4t + t2 = 4 + 0.49 Combine like terms: 4 + 0.49 = 4.49 0.49 + -1.4t + t2 = 4.49 Factor a perfect square on the left side: (t + -0.7)(t + -0.7) = 4.49 Calculate the square root of the right side: 2.11896201 Break this problem into two subproblems by setting (t + -0.7) equal to 2.11896201 and -2.11896201.Subproblem 1
t + -0.7 = 2.11896201 Simplifying t + -0.7 = 2.11896201 Reorder the terms: -0.7 + t = 2.11896201 Solving -0.7 + t = 2.11896201 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + t = 2.11896201 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = 2.11896201 + 0.7 t = 2.11896201 + 0.7 Combine like terms: 2.11896201 + 0.7 = 2.81896201 t = 2.81896201 Simplifying t = 2.81896201Subproblem 2
t + -0.7 = -2.11896201 Simplifying t + -0.7 = -2.11896201 Reorder the terms: -0.7 + t = -2.11896201 Solving -0.7 + t = -2.11896201 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + t = -2.11896201 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = -2.11896201 + 0.7 t = -2.11896201 + 0.7 Combine like terms: -2.11896201 + 0.7 = -1.41896201 t = -1.41896201 Simplifying t = -1.41896201Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.81896201, -1.41896201}
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