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Simplifying 4t2 + -28t + 15 = 0 Reorder the terms: 15 + -28t + 4t2 = 0 Solving 15 + -28t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -7t + t2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -7t + -3.75 + t2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -7t + t2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -7t + t2 = 0 + -3.75 -7t + t2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -7t + t2 = -3.75 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = -3.75 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -3.75 + 12.25 Combine like terms: -3.75 + 12.25 = 8.5 12.25 + -7t + t2 = 8.5 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (t + -3.5) equal to 2.915475947 and -2.915475947.Subproblem 1
t + -3.5 = 2.915475947 Simplifying t + -3.5 = 2.915475947 Reorder the terms: -3.5 + t = 2.915475947 Solving -3.5 + t = 2.915475947 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 2.915475947 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 2.915475947 + 3.5 t = 2.915475947 + 3.5 Combine like terms: 2.915475947 + 3.5 = 6.415475947 t = 6.415475947 Simplifying t = 6.415475947Subproblem 2
t + -3.5 = -2.915475947 Simplifying t + -3.5 = -2.915475947 Reorder the terms: -3.5 + t = -2.915475947 Solving -3.5 + t = -2.915475947 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -2.915475947 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -2.915475947 + 3.5 t = -2.915475947 + 3.5 Combine like terms: -2.915475947 + 3.5 = 0.584524053 t = 0.584524053 Simplifying t = 0.584524053Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.415475947, 0.584524053}
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