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Simplifying t2 + -24t + 7 = 0 Reorder the terms: 7 + -24t + t2 = 0 Solving 7 + -24t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -24t + -7 + t2 = 0 + -7 Reorder the terms: 7 + -7 + -24t + t2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -24t + t2 = 0 + -7 -24t + t2 = 0 + -7 Combine like terms: 0 + -7 = -7 -24t + t2 = -7 The t term is -24t. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24t + 144 + t2 = -7 + 144 Reorder the terms: 144 + -24t + t2 = -7 + 144 Combine like terms: -7 + 144 = 137 144 + -24t + t2 = 137 Factor a perfect square on the left side: (t + -12)(t + -12) = 137 Calculate the square root of the right side: 11.704699911 Break this problem into two subproblems by setting (t + -12) equal to 11.704699911 and -11.704699911.Subproblem 1
t + -12 = 11.704699911 Simplifying t + -12 = 11.704699911 Reorder the terms: -12 + t = 11.704699911 Solving -12 + t = 11.704699911 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = 11.704699911 + 12 Combine like terms: -12 + 12 = 0 0 + t = 11.704699911 + 12 t = 11.704699911 + 12 Combine like terms: 11.704699911 + 12 = 23.704699911 t = 23.704699911 Simplifying t = 23.704699911Subproblem 2
t + -12 = -11.704699911 Simplifying t + -12 = -11.704699911 Reorder the terms: -12 + t = -11.704699911 Solving -12 + t = -11.704699911 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = -11.704699911 + 12 Combine like terms: -12 + 12 = 0 0 + t = -11.704699911 + 12 t = -11.704699911 + 12 Combine like terms: -11.704699911 + 12 = 0.295300089 t = 0.295300089 Simplifying t = 0.295300089Solution
The solution to the problem is based on the solutions from the subproblems. t = {23.704699911, 0.295300089}
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