(t+2)(t+2)+(t-3)(t-3)=9

Solution for (t+2)(t+2)+(t-3)(t-3)=9 equation:

Simplifying
(t + 2)(t + 2) + (t + -3)(t + -3) = 9

Reorder the terms:
(2 + t)(t + 2) + (t + -3)(t + -3) = 9

Reorder the terms:
(2 + t)(2 + t) + (t + -3)(t + -3) = 9

Multiply (2 + t) * (2 + t)
(2(2 + t) + t(2 + t)) + (t + -3)(t + -3) = 9
((2 * 2 + t * 2) + t(2 + t)) + (t + -3)(t + -3) = 9
((4 + 2t) + t(2 + t)) + (t + -3)(t + -3) = 9
(4 + 2t + (2 * t + t * t)) + (t + -3)(t + -3) = 9
(4 + 2t + (2t + t2)) + (t + -3)(t + -3) = 9

Combine like terms: 2t + 2t = 4t
(4 + 4t + t2) + (t + -3)(t + -3) = 9

Reorder the terms:
4 + 4t + t2 + (-3 + t)(t + -3) = 9

Reorder the terms:
4 + 4t + t2 + (-3 + t)(-3 + t) = 9

Multiply (-3 + t) * (-3 + t)
4 + 4t + t2 + (-3(-3 + t) + t(-3 + t)) = 9
4 + 4t + t2 + ((-3 * -3 + t * -3) + t(-3 + t)) = 9
4 + 4t + t2 + ((9 + -3t) + t(-3 + t)) = 9
4 + 4t + t2 + (9 + -3t + (-3 * t + t * t)) = 9
4 + 4t + t2 + (9 + -3t + (-3t + t2)) = 9

Combine like terms: -3t + -3t = -6t
4 + 4t + t2 + (9 + -6t + t2) = 9

Reorder the terms:
4 + 9 + 4t + -6t + t2 + t2 = 9

Combine like terms: 4 + 9 = 13
13 + 4t + -6t + t2 + t2 = 9

Combine like terms: 4t + -6t = -2t
13 + -2t + t2 + t2 = 9

Combine like terms: t2 + t2 = 2t2
13 + -2t + 2t2 = 9

Solving
13 + -2t + 2t2 = 9

Solving for variable 't'.

Reorder the terms:
13 + -9 + -2t + 2t2 = 9 + -9

Combine like terms: 13 + -9 = 4
4 + -2t + 2t2 = 9 + -9

Combine like terms: 9 + -9 = 0
4 + -2t + 2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -1t + t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -1t + t2)' equal to zero and attempt to solve:

Simplifying
2 + -1t + t2 = 0

Solving
2 + -1t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1t + -2 + t2 = 0 + -2

Reorder the terms:
2 + -2 + -1t + t2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t + t2 = 0 + -2
-1t + t2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1t + t2 = -2

The t term is -1t.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = -2 + 0.25

Reorder the terms:
0.25 + -1t + t2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + -1t + t2 = -1.75

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.