0=100t^2-15400t+11700

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Solution for 0=100t^2-15400t+11700 equation:


Simplifying
0 = 100t2 + -15400t + 11700

Reorder the terms:
0 = 11700 + -15400t + 100t2

Solving
0 = 11700 + -15400t + 100t2

Solving for variable 't'.

Combine like terms: 0 + -11700 = -11700
-11700 + 15400t + -100t2 = 11700 + -15400t + 100t2 + -11700 + 15400t + -100t2

Reorder the terms:
-11700 + 15400t + -100t2 = 11700 + -11700 + -15400t + 15400t + 100t2 + -100t2

Combine like terms: 11700 + -11700 = 0
-11700 + 15400t + -100t2 = 0 + -15400t + 15400t + 100t2 + -100t2
-11700 + 15400t + -100t2 = -15400t + 15400t + 100t2 + -100t2

Combine like terms: -15400t + 15400t = 0
-11700 + 15400t + -100t2 = 0 + 100t2 + -100t2
-11700 + 15400t + -100t2 = 100t2 + -100t2

Combine like terms: 100t2 + -100t2 = 0
-11700 + 15400t + -100t2 = 0

Factor out the Greatest Common Factor (GCF), '100'.
100(-117 + 154t + -1t2) = 0

Ignore the factor 100.

Subproblem 1

Set the factor '(-117 + 154t + -1t2)' equal to zero and attempt to solve: Simplifying -117 + 154t + -1t2 = 0 Solving -117 + 154t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 117 + -154t + t2 = 0 Move the constant term to the right: Add '-117' to each side of the equation. 117 + -154t + -117 + t2 = 0 + -117 Reorder the terms: 117 + -117 + -154t + t2 = 0 + -117 Combine like terms: 117 + -117 = 0 0 + -154t + t2 = 0 + -117 -154t + t2 = 0 + -117 Combine like terms: 0 + -117 = -117 -154t + t2 = -117 The t term is -154t. Take half its coefficient (-77). Square it (5929) and add it to both sides. Add '5929' to each side of the equation. -154t + 5929 + t2 = -117 + 5929 Reorder the terms: 5929 + -154t + t2 = -117 + 5929 Combine like terms: -117 + 5929 = 5812 5929 + -154t + t2 = 5812 Factor a perfect square on the left side: (t + -77)(t + -77) = 5812 Calculate the square root of the right side: 76.23647421 Break this problem into two subproblems by setting (t + -77) equal to 76.23647421 and -76.23647421.

Subproblem 1

t + -77 = 76.23647421 Simplifying t + -77 = 76.23647421 Reorder the terms: -77 + t = 76.23647421 Solving -77 + t = 76.23647421 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '77' to each side of the equation. -77 + 77 + t = 76.23647421 + 77 Combine like terms: -77 + 77 = 0 0 + t = 76.23647421 + 77 t = 76.23647421 + 77 Combine like terms: 76.23647421 + 77 = 153.23647421 t = 153.23647421 Simplifying t = 153.23647421

Subproblem 2

t + -77 = -76.23647421 Simplifying t + -77 = -76.23647421 Reorder the terms: -77 + t = -76.23647421 Solving -77 + t = -76.23647421 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '77' to each side of the equation. -77 + 77 + t = -76.23647421 + 77 Combine like terms: -77 + 77 = 0 0 + t = -76.23647421 + 77 t = -76.23647421 + 77 Combine like terms: -76.23647421 + 77 = 0.76352579 t = 0.76352579 Simplifying t = 0.76352579

Solution

The solution to the problem is based on the solutions from the subproblems. t = {153.23647421, 0.76352579}

Solution

t = {153.23647421, 0.76352579}

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