(8-7t)+(t^2-1)=0

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Solution for (8-7t)+(t^2-1)=0 equation:


Simplifying
(8 + -7t) + (t2 + -1) = 0

Remove parenthesis around (8 + -7t)
8 + -7t + (t2 + -1) = 0

Reorder the terms:
8 + -7t + (-1 + t2) = 0

Remove parenthesis around (-1 + t2)
8 + -7t + -1 + t2 = 0

Reorder the terms:
8 + -1 + -7t + t2 = 0

Combine like terms: 8 + -1 = 7
7 + -7t + t2 = 0

Solving
7 + -7t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -7t + -7 + t2 = 0 + -7

Reorder the terms:
7 + -7 + -7t + t2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -7t + t2 = 0 + -7
-7t + t2 = 0 + -7

Combine like terms: 0 + -7 = -7
-7t + t2 = -7

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = -7 + 12.25

Reorder the terms:
12.25 + -7t + t2 = -7 + 12.25

Combine like terms: -7 + 12.25 = 5.25
12.25 + -7t + t2 = 5.25

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(t + -3.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

t + -3.5 = 2.291287847 Simplifying t + -3.5 = 2.291287847 Reorder the terms: -3.5 + t = 2.291287847 Solving -3.5 + t = 2.291287847 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 2.291287847 + 3.5 t = 2.291287847 + 3.5 Combine like terms: 2.291287847 + 3.5 = 5.791287847 t = 5.791287847 Simplifying t = 5.791287847

Subproblem 2

t + -3.5 = -2.291287847 Simplifying t + -3.5 = -2.291287847 Reorder the terms: -3.5 + t = -2.291287847 Solving -3.5 + t = -2.291287847 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -2.291287847 + 3.5 t = -2.291287847 + 3.5 Combine like terms: -2.291287847 + 3.5 = 1.208712153 t = 1.208712153 Simplifying t = 1.208712153

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.791287847, 1.208712153}

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