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Simplifying t2 + 10t + -130 = 0 Reorder the terms: -130 + 10t + t2 = 0 Solving -130 + 10t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + 10t + 130 + t2 = 0 + 130 Reorder the terms: -130 + 130 + 10t + t2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 10t + t2 = 0 + 130 10t + t2 = 0 + 130 Combine like terms: 0 + 130 = 130 10t + t2 = 130 The t term is 10t. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10t + 25 + t2 = 130 + 25 Reorder the terms: 25 + 10t + t2 = 130 + 25 Combine like terms: 130 + 25 = 155 25 + 10t + t2 = 155 Factor a perfect square on the left side: (t + 5)(t + 5) = 155 Calculate the square root of the right side: 12.449899598 Break this problem into two subproblems by setting (t + 5) equal to 12.449899598 and -12.449899598.Subproblem 1
t + 5 = 12.449899598 Simplifying t + 5 = 12.449899598 Reorder the terms: 5 + t = 12.449899598 Solving 5 + t = 12.449899598 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 12.449899598 + -5 Combine like terms: 5 + -5 = 0 0 + t = 12.449899598 + -5 t = 12.449899598 + -5 Combine like terms: 12.449899598 + -5 = 7.449899598 t = 7.449899598 Simplifying t = 7.449899598Subproblem 2
t + 5 = -12.449899598 Simplifying t + 5 = -12.449899598 Reorder the terms: 5 + t = -12.449899598 Solving 5 + t = -12.449899598 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -12.449899598 + -5 Combine like terms: 5 + -5 = 0 0 + t = -12.449899598 + -5 t = -12.449899598 + -5 Combine like terms: -12.449899598 + -5 = -17.449899598 t = -17.449899598 Simplifying t = -17.449899598Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.449899598, -17.449899598}
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