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Simplifying 96t4 + -625t2 = 225 Reorder the terms: -625t2 + 96t4 = 225 Solving -625t2 + 96t4 = 225 Solving for variable 't'. Reorder the terms: -225 + -625t2 + 96t4 = 225 + -225 Combine like terms: 225 + -225 = 0 -225 + -625t2 + 96t4 = 0 Begin completing the square. Divide all terms by 96 the coefficient of the squared term: Divide each side by '96'. -2.34375 + -6.510416667t2 + t4 = 0 Move the constant term to the right: Add '2.34375' to each side of the equation. -2.34375 + -6.510416667t2 + 2.34375 + t4 = 0 + 2.34375 Reorder the terms: -2.34375 + 2.34375 + -6.510416667t2 + t4 = 0 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + -6.510416667t2 + t4 = 0 + 2.34375 -6.510416667t2 + t4 = 0 + 2.34375 Combine like terms: 0 + 2.34375 = 2.34375 -6.510416667t2 + t4 = 2.34375 The t term is -6.510416667t2. Take half its coefficient (-3.255208334). Square it (10.59638130) and add it to both sides. Add '10.59638130' to each side of the equation. -6.510416667t2 + 10.59638130 + t4 = 2.34375 + 10.59638130 Reorder the terms: 10.59638130 + -6.510416667t2 + t4 = 2.34375 + 10.59638130 Combine like terms: 2.34375 + 10.59638130 = 12.9401313 10.59638130 + -6.510416667t2 + t4 = 12.9401313 Factor a perfect square on the left side: (t2 + -3.255208334)(t2 + -3.255208334) = 12.9401313 Calculate the square root of the right side: 3.5972394 Break this problem into two subproblems by setting (t2 + -3.255208334) equal to 3.5972394 and -3.5972394.Subproblem 1
t2 + -3.255208334 = 3.5972394 Simplifying t2 + -3.255208334 = 3.5972394 Reorder the terms: -3.255208334 + t2 = 3.5972394 Solving -3.255208334 + t2 = 3.5972394 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.255208334' to each side of the equation. -3.255208334 + 3.255208334 + t2 = 3.5972394 + 3.255208334 Combine like terms: -3.255208334 + 3.255208334 = 0.000000000 0.000000000 + t2 = 3.5972394 + 3.255208334 t2 = 3.5972394 + 3.255208334 Combine like terms: 3.5972394 + 3.255208334 = 6.852447734 t2 = 6.852447734 Simplifying t2 = 6.852447734 Take the square root of each side: t = {-2.617718039, 2.617718039}Subproblem 2
t2 + -3.255208334 = -3.5972394 Simplifying t2 + -3.255208334 = -3.5972394 Reorder the terms: -3.255208334 + t2 = -3.5972394 Solving -3.255208334 + t2 = -3.5972394 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.255208334' to each side of the equation. -3.255208334 + 3.255208334 + t2 = -3.5972394 + 3.255208334 Combine like terms: -3.255208334 + 3.255208334 = 0.000000000 0.000000000 + t2 = -3.5972394 + 3.255208334 t2 = -3.5972394 + 3.255208334 Combine like terms: -3.5972394 + 3.255208334 = -0.342031066 t2 = -0.342031066 Simplifying t2 = -0.342031066 Reorder the terms: 0.342031066 + t2 = -0.342031066 + 0.342031066 Combine like terms: -0.342031066 + 0.342031066 = 0.000000000 0.342031066 + t2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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