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Simplifying -5t2 + 20t + 100 = 0 Reorder the terms: 100 + 20t + -5t2 = 0 Solving 100 + 20t + -5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(20 + 4t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(20 + 4t + -1t2)' equal to zero and attempt to solve: Simplifying 20 + 4t + -1t2 = 0 Solving 20 + 4t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + -4t + t2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -4t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + -4t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -4t + t2 = 0 + 20 -4t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 -4t + t2 = 20 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 20 + 4 Reorder the terms: 4 + -4t + t2 = 20 + 4 Combine like terms: 20 + 4 = 24 4 + -4t + t2 = 24 Factor a perfect square on the left side: (t + -2)(t + -2) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (t + -2) equal to 4.898979486 and -4.898979486.Subproblem 1
t + -2 = 4.898979486 Simplifying t + -2 = 4.898979486 Reorder the terms: -2 + t = 4.898979486 Solving -2 + t = 4.898979486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + t = 4.898979486 + 2 t = 4.898979486 + 2 Combine like terms: 4.898979486 + 2 = 6.898979486 t = 6.898979486 Simplifying t = 6.898979486Subproblem 2
t + -2 = -4.898979486 Simplifying t + -2 = -4.898979486 Reorder the terms: -2 + t = -4.898979486 Solving -2 + t = -4.898979486 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -4.898979486 + 2 Combine like terms: -2 + 2 = 0 0 + t = -4.898979486 + 2 t = -4.898979486 + 2 Combine like terms: -4.898979486 + 2 = -2.898979486 t = -2.898979486 Simplifying t = -2.898979486Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.898979486, -2.898979486}Solution
t = {6.898979486, -2.898979486}
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