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Simplifying 325 = 17.6t + 0.528t2 Solving 325 = 17.6t + 0.528t2 Solving for variable 't'. Reorder the terms: 325 + -17.6t + -0.528t2 = 17.6t + -17.6t + 0.528t2 + -0.528t2 Combine like terms: 17.6t + -17.6t = 0.0 325 + -17.6t + -0.528t2 = 0.0 + 0.528t2 + -0.528t2 325 + -17.6t + -0.528t2 = 0.528t2 + -0.528t2 Combine like terms: 0.528t2 + -0.528t2 = 0.000 325 + -17.6t + -0.528t2 = 0.000 Begin completing the square. Divide all terms by -0.528 the coefficient of the squared term: Divide each side by '-0.528'. -615.530303 + 33.33333333t + t2 = 0 Move the constant term to the right: Add '615.530303' to each side of the equation. -615.530303 + 33.33333333t + 615.530303 + t2 = 0 + 615.530303 Reorder the terms: -615.530303 + 615.530303 + 33.33333333t + t2 = 0 + 615.530303 Combine like terms: -615.530303 + 615.530303 = 0.000000 0.000000 + 33.33333333t + t2 = 0 + 615.530303 33.33333333t + t2 = 0 + 615.530303 Combine like terms: 0 + 615.530303 = 615.530303 33.33333333t + t2 = 615.530303 The t term is 33.33333333t. Take half its coefficient (16.66666667). Square it (277.7777779) and add it to both sides. Add '277.7777779' to each side of the equation. 33.33333333t + 277.7777779 + t2 = 615.530303 + 277.7777779 Reorder the terms: 277.7777779 + 33.33333333t + t2 = 615.530303 + 277.7777779 Combine like terms: 615.530303 + 277.7777779 = 893.3080809 277.7777779 + 33.33333333t + t2 = 893.3080809 Factor a perfect square on the left side: (t + 16.66666667)(t + 16.66666667) = 893.3080809 Calculate the square root of the right side: 29.888259918 Break this problem into two subproblems by setting (t + 16.66666667) equal to 29.888259918 and -29.888259918.Subproblem 1
t + 16.66666667 = 29.888259918 Simplifying t + 16.66666667 = 29.888259918 Reorder the terms: 16.66666667 + t = 29.888259918 Solving 16.66666667 + t = 29.888259918 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + t = 29.888259918 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + t = 29.888259918 + -16.66666667 t = 29.888259918 + -16.66666667 Combine like terms: 29.888259918 + -16.66666667 = 13.221593248 t = 13.221593248 Simplifying t = 13.221593248Subproblem 2
t + 16.66666667 = -29.888259918 Simplifying t + 16.66666667 = -29.888259918 Reorder the terms: 16.66666667 + t = -29.888259918 Solving 16.66666667 + t = -29.888259918 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16.66666667' to each side of the equation. 16.66666667 + -16.66666667 + t = -29.888259918 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + t = -29.888259918 + -16.66666667 t = -29.888259918 + -16.66666667 Combine like terms: -29.888259918 + -16.66666667 = -46.554926588 t = -46.554926588 Simplifying t = -46.554926588Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.221593248, -46.554926588}
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