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Simplifying 4t + t2 + -20 = 0 Reorder the terms: -20 + 4t + t2 = 0 Solving -20 + 4t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 4t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + 4t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 4t + t2 = 0 + 20 4t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 4t + t2 = 20 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = 20 + 4 Reorder the terms: 4 + 4t + t2 = 20 + 4 Combine like terms: 20 + 4 = 24 4 + 4t + t2 = 24 Factor a perfect square on the left side: (t + 2)(t + 2) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (t + 2) equal to 4.898979486 and -4.898979486.Subproblem 1
t + 2 = 4.898979486 Simplifying t + 2 = 4.898979486 Reorder the terms: 2 + t = 4.898979486 Solving 2 + t = 4.898979486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 4.898979486 + -2 Combine like terms: 2 + -2 = 0 0 + t = 4.898979486 + -2 t = 4.898979486 + -2 Combine like terms: 4.898979486 + -2 = 2.898979486 t = 2.898979486 Simplifying t = 2.898979486Subproblem 2
t + 2 = -4.898979486 Simplifying t + 2 = -4.898979486 Reorder the terms: 2 + t = -4.898979486 Solving 2 + t = -4.898979486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -4.898979486 + -2 Combine like terms: 2 + -2 = 0 0 + t = -4.898979486 + -2 t = -4.898979486 + -2 Combine like terms: -4.898979486 + -2 = -6.898979486 t = -6.898979486 Simplifying t = -6.898979486Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.898979486, -6.898979486}
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