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Simplifying 24.059t4 + -5625t2 + 10000 = 0 Reorder the terms: 10000 + -5625t2 + 24.059t4 = 0 Solving 10000 + -5625t2 + 24.059t4 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 24.059 the coefficient of the squared term: Divide each side by '24.059'. 415.644873 + -233.8002411t2 + t4 = 0 Move the constant term to the right: Add '-415.644873' to each side of the equation. 415.644873 + -233.8002411t2 + -415.644873 + t4 = 0 + -415.644873 Reorder the terms: 415.644873 + -415.644873 + -233.8002411t2 + t4 = 0 + -415.644873 Combine like terms: 415.644873 + -415.644873 = 0.000000 0.000000 + -233.8002411t2 + t4 = 0 + -415.644873 -233.8002411t2 + t4 = 0 + -415.644873 Combine like terms: 0 + -415.644873 = -415.644873 -233.8002411t2 + t4 = -415.644873 The t term is -233.8002411t2. Take half its coefficient (-116.9001206). Square it (13665.63820) and add it to both sides. Add '13665.63820' to each side of the equation. -233.8002411t2 + 13665.63820 + t4 = -415.644873 + 13665.63820 Reorder the terms: 13665.63820 + -233.8002411t2 + t4 = -415.644873 + 13665.63820 Combine like terms: -415.644873 + 13665.63820 = 13249.993327 13665.63820 + -233.8002411t2 + t4 = 13249.993327 Factor a perfect square on the left side: (t2 + -116.9001206)(t2 + -116.9001206) = 13249.993327 Calculate the square root of the right side: 115.108615347 Break this problem into two subproblems by setting (t2 + -116.9001206) equal to 115.108615347 and -115.108615347.Subproblem 1
t2 + -116.9001206 = 115.108615347 Simplifying t2 + -116.9001206 = 115.108615347 Reorder the terms: -116.9001206 + t2 = 115.108615347 Solving -116.9001206 + t2 = 115.108615347 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '116.9001206' to each side of the equation. -116.9001206 + 116.9001206 + t2 = 115.108615347 + 116.9001206 Combine like terms: -116.9001206 + 116.9001206 = 0.0000000 0.0000000 + t2 = 115.108615347 + 116.9001206 t2 = 115.108615347 + 116.9001206 Combine like terms: 115.108615347 + 116.9001206 = 232.008735947 t2 = 232.008735947 Simplifying t2 = 232.008735947 Take the square root of each side: t = {-15.231832981, 15.231832981}Subproblem 2
t2 + -116.9001206 = -115.108615347 Simplifying t2 + -116.9001206 = -115.108615347 Reorder the terms: -116.9001206 + t2 = -115.108615347 Solving -116.9001206 + t2 = -115.108615347 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '116.9001206' to each side of the equation. -116.9001206 + 116.9001206 + t2 = -115.108615347 + 116.9001206 Combine like terms: -116.9001206 + 116.9001206 = 0.0000000 0.0000000 + t2 = -115.108615347 + 116.9001206 t2 = -115.108615347 + 116.9001206 Combine like terms: -115.108615347 + 116.9001206 = 1.791505253 t2 = 1.791505253 Simplifying t2 = 1.791505253 Take the square root of each side: t = {-1.338471237, 1.338471237}Solution
The solution to the problem is based on the solutions from the subproblems. t = {-15.231832981, 15.231832981, -1.338471237, 1.338471237}
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