Question $4 t-2+t^{2}=6+t^{2}$

Studdy Solution

STEP 1

1. The equation $4t - 2 + t^2 = 6 + t^2$ is a quadratic equation.
2. The goal is to solve for the variable $t$ .
3. The equation involves basic algebraic operations and simplification.

STEP 2

1. Simplify the equation by eliminating like terms.
2. Isolate the variable $t$ by performing algebraic operations.
3. Solve for $t$ .
4. Verify the solution by substituting it back into the original equation.

STEP 3

First, simplify the equation by eliminating the $t^2$ terms on both sides:
$4t - 2 + t^2 = 6 + t^2$
Subtract $t^2$ from both sides:
$4t - 2 = 6$

STEP 4

Now, isolate the variable $t$ by performing algebraic operations. Start by adding 2 to both sides:
$4t - 2 + 2 = 6 + 2$
This simplifies to:
$4t = 8$

STEP 5

Next, divide both sides by 4 to solve for $t$ :
$\frac{4t}{4} = \frac{8}{4}$
This simplifies to:
$t = 2$

STEP 6

Verify the solution by substituting $t = 2$ back into the original equation:
Original equation: $4t - 2 + t^2 = 6 + t^2$
Substitute $t = 2$ :
$4(2) - 2 + 2^2 = 6 + 2^2$
Simplify both sides:
$8 - 2 + 4 = 6 + 4$
$10 = 10$
Both sides are equal, confirming the solution.
The solution is:
$\boxed{2}$

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