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Simplifying 6t2 + 10t + -15 = 0 Reorder the terms: -15 + 10t + 6t2 = 0 Solving -15 + 10t + 6t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.5 + 1.666666667t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 1.666666667t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 1.666666667t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 1.666666667t + t2 = 0 + 2.5 1.666666667t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 1.666666667t + t2 = 2.5 The t term is 1.666666667t. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667t + 0.6944444447 + t2 = 2.5 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667t + t2 = 2.5 + 0.6944444447 Combine like terms: 2.5 + 0.6944444447 = 3.1944444447 0.6944444447 + 1.666666667t + t2 = 3.1944444447 Factor a perfect square on the left side: (t + 0.8333333335)(t + 0.8333333335) = 3.1944444447 Calculate the square root of the right side: 1.787300883 Break this problem into two subproblems by setting (t + 0.8333333335) equal to 1.787300883 and -1.787300883.Subproblem 1
t + 0.8333333335 = 1.787300883 Simplifying t + 0.8333333335 = 1.787300883 Reorder the terms: 0.8333333335 + t = 1.787300883 Solving 0.8333333335 + t = 1.787300883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + t = 1.787300883 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + t = 1.787300883 + -0.8333333335 t = 1.787300883 + -0.8333333335 Combine like terms: 1.787300883 + -0.8333333335 = 0.9539675495 t = 0.9539675495 Simplifying t = 0.9539675495Subproblem 2
t + 0.8333333335 = -1.787300883 Simplifying t + 0.8333333335 = -1.787300883 Reorder the terms: 0.8333333335 + t = -1.787300883 Solving 0.8333333335 + t = -1.787300883 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + t = -1.787300883 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + t = -1.787300883 + -0.8333333335 t = -1.787300883 + -0.8333333335 Combine like terms: -1.787300883 + -0.8333333335 = -2.6206342165 t = -2.6206342165 Simplifying t = -2.6206342165Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.9539675495, -2.6206342165}
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