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Simplifying 1400 = 5t2 + 5t + 7 Reorder the terms: 1400 = 7 + 5t + 5t2 Solving 1400 = 7 + 5t + 5t2 Solving for variable 't'. Combine like terms: 1400 + -7 = 1393 1393 + -5t + -5t2 = 7 + 5t + 5t2 + -7 + -5t + -5t2 Reorder the terms: 1393 + -5t + -5t2 = 7 + -7 + 5t + -5t + 5t2 + -5t2 Combine like terms: 7 + -7 = 0 1393 + -5t + -5t2 = 0 + 5t + -5t + 5t2 + -5t2 1393 + -5t + -5t2 = 5t + -5t + 5t2 + -5t2 Combine like terms: 5t + -5t = 0 1393 + -5t + -5t2 = 0 + 5t2 + -5t2 1393 + -5t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 1393 + -5t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -278.6 + t + t2 = 0 Move the constant term to the right: Add '278.6' to each side of the equation. -278.6 + t + 278.6 + t2 = 0 + 278.6 Reorder the terms: -278.6 + 278.6 + t + t2 = 0 + 278.6 Combine like terms: -278.6 + 278.6 = 0.0 0.0 + t + t2 = 0 + 278.6 t + t2 = 0 + 278.6 Combine like terms: 0 + 278.6 = 278.6 t + t2 = 278.6 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 278.6 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 278.6 + 0.25 Combine like terms: 278.6 + 0.25 = 278.85 1.25 + t2 = 278.85 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 278.85 Calculate the square root of the right side: 16.698802352 Break this problem into two subproblems by setting (t + 0.5) equal to 16.698802352 and -16.698802352.Subproblem 1
t + 0.5 = 16.698802352 Simplifying t + 0.5 = 16.698802352 Reorder the terms: 0.5 + t = 16.698802352 Solving 0.5 + t = 16.698802352 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 16.698802352 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 16.698802352 + -0.5 t = 16.698802352 + -0.5 Combine like terms: 16.698802352 + -0.5 = 16.198802352 t = 16.198802352 Simplifying t = 16.198802352Subproblem 2
t + 0.5 = -16.698802352 Simplifying t + 0.5 = -16.698802352 Reorder the terms: 0.5 + t = -16.698802352 Solving 0.5 + t = -16.698802352 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -16.698802352 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -16.698802352 + -0.5 t = -16.698802352 + -0.5 Combine like terms: -16.698802352 + -0.5 = -17.198802352 t = -17.198802352 Simplifying t = -17.198802352Solution
The solution to the problem is based on the solutions from the subproblems. t = {16.198802352, -17.198802352}
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