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Simplifying t2 + 4t + -91 = 0 Reorder the terms: -91 + 4t + t2 = 0 Solving -91 + 4t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + 4t + 91 + t2 = 0 + 91 Reorder the terms: -91 + 91 + 4t + t2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + 4t + t2 = 0 + 91 4t + t2 = 0 + 91 Combine like terms: 0 + 91 = 91 4t + t2 = 91 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 = 91 + 4 Reorder the terms: 4 + 4t + t2 = 91 + 4 Combine like terms: 91 + 4 = 95 4 + 4t + t2 = 95 Factor a perfect square on the left side: (t + 2)(t + 2) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (t + 2) equal to 9.746794345 and -9.746794345.Subproblem 1
t + 2 = 9.746794345 Simplifying t + 2 = 9.746794345 Reorder the terms: 2 + t = 9.746794345 Solving 2 + t = 9.746794345 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 = 9.746794345 + -2 Combine like terms: 2 + -2 = 0 0 + t = 9.746794345 + -2 t = 9.746794345 + -2 Combine like terms: 9.746794345 + -2 = 7.746794345 t = 7.746794345 Simplifying t = 7.746794345Subproblem 2
t + 2 = -9.746794345 Simplifying t + 2 = -9.746794345 Reorder the terms: 2 + t = -9.746794345 Solving 2 + t = -9.746794345 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 = -9.746794345 + -2 Combine like terms: 2 + -2 = 0 0 + t = -9.746794345 + -2 t = -9.746794345 + -2 Combine like terms: -9.746794345 + -2 = -11.746794345 t = -11.746794345 Simplifying t = -11.746794345Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.746794345, -11.746794345}
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