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Simplifying -3(t2 + 14t + -14) = 0 Reorder the terms: -3(-14 + 14t + t2) = 0 (-14 * -3 + 14t * -3 + t2 * -3) = 0 (42 + -42t + -3t2) = 0 Solving 42 + -42t + -3t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + -14t + -1t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(14 + -14t + -1t2)' equal to zero and attempt to solve: Simplifying 14 + -14t + -1t2 = 0 Solving 14 + -14t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + 14t + t2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 14t + 14 + t2 = 0 + 14 Reorder the terms: -14 + 14 + 14t + t2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 14t + t2 = 0 + 14 14t + t2 = 0 + 14 Combine like terms: 0 + 14 = 14 14t + t2 = 14 The t term is 14t. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14t + 49 + t2 = 14 + 49 Reorder the terms: 49 + 14t + t2 = 14 + 49 Combine like terms: 14 + 49 = 63 49 + 14t + t2 = 63 Factor a perfect square on the left side: (t + 7)(t + 7) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (t + 7) equal to 7.937253933 and -7.937253933.Subproblem 1
t + 7 = 7.937253933 Simplifying t + 7 = 7.937253933 Reorder the terms: 7 + t = 7.937253933 Solving 7 + t = 7.937253933 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + t = 7.937253933 + -7 Combine like terms: 7 + -7 = 0 0 + t = 7.937253933 + -7 t = 7.937253933 + -7 Combine like terms: 7.937253933 + -7 = 0.937253933 t = 0.937253933 Simplifying t = 0.937253933Subproblem 2
t + 7 = -7.937253933 Simplifying t + 7 = -7.937253933 Reorder the terms: 7 + t = -7.937253933 Solving 7 + t = -7.937253933 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + t = -7.937253933 + -7 Combine like terms: 7 + -7 = 0 0 + t = -7.937253933 + -7 t = -7.937253933 + -7 Combine like terms: -7.937253933 + -7 = -14.937253933 t = -14.937253933 Simplifying t = -14.937253933Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.937253933, -14.937253933}Solution
t = {0.937253933, -14.937253933}
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