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Simplifying 5t2 + -4t + -86 = 0 Reorder the terms: -86 + -4t + 5t2 = 0 Solving -86 + -4t + 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'. -17.2 + -0.8t + t2 = 0 Move the constant term to the right: Add '17.2' to each side of the equation. -17.2 + -0.8t + 17.2 + t2 = 0 + 17.2 Reorder the terms: -17.2 + 17.2 + -0.8t + t2 = 0 + 17.2 Combine like terms: -17.2 + 17.2 = 0.0 0.0 + -0.8t + t2 = 0 + 17.2 -0.8t + t2 = 0 + 17.2 Combine like terms: 0 + 17.2 = 17.2 -0.8t + t2 = 17.2 The t term is -0.8t. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8t + 0.16 + t2 = 17.2 + 0.16 Reorder the terms: 0.16 + -0.8t + t2 = 17.2 + 0.16 Combine like terms: 17.2 + 0.16 = 17.36 0.16 + -0.8t + t2 = 17.36 Factor a perfect square on the left side: (t + -0.4)(t + -0.4) = 17.36 Calculate the square root of the right side: 4.166533331 Break this problem into two subproblems by setting (t + -0.4) equal to 4.166533331 and -4.166533331.Subproblem 1
t + -0.4 = 4.166533331 Simplifying t + -0.4 = 4.166533331 Reorder the terms: -0.4 + t = 4.166533331 Solving -0.4 + t = 4.166533331 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = 4.166533331 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = 4.166533331 + 0.4 t = 4.166533331 + 0.4 Combine like terms: 4.166533331 + 0.4 = 4.566533331 t = 4.566533331 Simplifying t = 4.566533331Subproblem 2
t + -0.4 = -4.166533331 Simplifying t + -0.4 = -4.166533331 Reorder the terms: -0.4 + t = -4.166533331 Solving -0.4 + t = -4.166533331 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = -4.166533331 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = -4.166533331 + 0.4 t = -4.166533331 + 0.4 Combine like terms: -4.166533331 + 0.4 = -3.766533331 t = -3.766533331 Simplifying t = -3.766533331Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.566533331, -3.766533331}
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