t^2+15t-6=0

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Solution for t^2+15t-6=0 equation:


Simplifying
t2 + 15t + -6 = 0

Reorder the terms:
-6 + 15t + t2 = 0

Solving
-6 + 15t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 15t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + 15t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 15t + t2 = 0 + 6
15t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
15t + t2 = 6

The t term is 15t.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15t + 56.25 + t2 = 6 + 56.25

Reorder the terms:
56.25 + 15t + t2 = 6 + 56.25

Combine like terms: 6 + 56.25 = 62.25
56.25 + 15t + t2 = 62.25

Factor a perfect square on the left side:
(t + 7.5)(t + 7.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(t + 7.5) equal to 7.889866919 and -7.889866919.

Subproblem 1

t + 7.5 = 7.889866919 Simplifying t + 7.5 = 7.889866919 Reorder the terms: 7.5 + t = 7.889866919 Solving 7.5 + t = 7.889866919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = 7.889866919 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = 7.889866919 + -7.5 t = 7.889866919 + -7.5 Combine like terms: 7.889866919 + -7.5 = 0.389866919 t = 0.389866919 Simplifying t = 0.389866919

Subproblem 2

t + 7.5 = -7.889866919 Simplifying t + 7.5 = -7.889866919 Reorder the terms: 7.5 + t = -7.889866919 Solving 7.5 + t = -7.889866919 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = -7.889866919 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = -7.889866919 + -7.5 t = -7.889866919 + -7.5 Combine like terms: -7.889866919 + -7.5 = -15.389866919 t = -15.389866919 Simplifying t = -15.389866919

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.389866919, -15.389866919}

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