t^2-17t=-15

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Solution for t^2-17t=-15 equation:


Simplifying
t2 + -17t = -15

Reorder the terms:
-17t + t2 = -15

Solving
-17t + t2 = -15

Solving for variable 't'.

Reorder the terms:
15 + -17t + t2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + -17t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -17t + -15 + t2 = 0 + -15

Reorder the terms:
15 + -15 + -17t + t2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -17t + t2 = 0 + -15
-17t + t2 = 0 + -15

Combine like terms: 0 + -15 = -15
-17t + t2 = -15

The t term is -17t.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17t + 72.25 + t2 = -15 + 72.25

Reorder the terms:
72.25 + -17t + t2 = -15 + 72.25

Combine like terms: -15 + 72.25 = 57.25
72.25 + -17t + t2 = 57.25

Factor a perfect square on the left side:
(t + -8.5)(t + -8.5) = 57.25

Calculate the square root of the right side: 7.566372975

Break this problem into two subproblems by setting 
(t + -8.5) equal to 7.566372975 and -7.566372975.

Subproblem 1

t + -8.5 = 7.566372975 Simplifying t + -8.5 = 7.566372975 Reorder the terms: -8.5 + t = 7.566372975 Solving -8.5 + t = 7.566372975 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + t = 7.566372975 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + t = 7.566372975 + 8.5 t = 7.566372975 + 8.5 Combine like terms: 7.566372975 + 8.5 = 16.066372975 t = 16.066372975 Simplifying t = 16.066372975

Subproblem 2

t + -8.5 = -7.566372975 Simplifying t + -8.5 = -7.566372975 Reorder the terms: -8.5 + t = -7.566372975 Solving -8.5 + t = -7.566372975 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + t = -7.566372975 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + t = -7.566372975 + 8.5 t = -7.566372975 + 8.5 Combine like terms: -7.566372975 + 8.5 = 0.933627025 t = 0.933627025 Simplifying t = 0.933627025

Solution

The solution to the problem is based on the solutions from the subproblems. t = {16.066372975, 0.933627025}

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