How do I solve for x in this math problem...?

3x² + x² = 19²

Add like terms, then square 19.
4x² = 361 (Divide both sides by 4)
x² = 361/4 (Square root)
√x² = √361/√4
x = 19/2 or 9.5

Checking:
3(9.5)² + (9.5)² = 19²
3(90.25) + 90.25 = 361
270.75 + 90.25 = 361
361 = 361

Thus, x = 19/2 or 9.5
Hope this helps.

3x² + x² = 19²
4x² = 19²
x² = 19²/4
x = ± 19/2

Answer: x = 19/2, - 19/2

Proof:
3(- 19/2²) + (- 19/2)² = 19²
3(361/4) + 361/4 = 361
1,083/4 + 361/4 = 361
1,444/4 = 361
361 = 361

The top answer looks good, except that its +19/2 or -19/2 (two roots).

3x^2 + x^2 = 19^2
add the coefficient of like terms
4 x^2 = 19^2
x^2 = (19/2)^2
x = +/- 19/2

3x^2 + x^2 = 19^2
4x^2 = 19^2
4x^2 - 19^2 = 0
(2x - 19)(2x + 19) = 0
2x - 19 =
2x = 19
x = 19/2 = 9.5
&
2x + 19 = 0
2x = -19
x = -19/2 = -9.5

a^2 - b^2 ≡ (a + b)(a - b)

3x^2 + x^2 = 19^2
4x^2 = 19^2
4x^2 - 19^2 = 0
(2x)^2 - 19^2 = 0
(2x + 19)(2x - 19) = 0

2x + 19 = 0
2x = -19
x = -19/2 (-9.5)

2x - 19 = 0
2x = 19
x = 19/2 (9.5)

∴ x = ±19/2 (±9.5)

3x^2 + x^2 = 19^2
4x ^2 = 19 ^2
Taking sq rt
2x = 19
Divide by 2
x = 19/2 (Answer)

19^2=361=4x^2 x^2=90.25 x>30

3x^2 + x^2 =19^2
(3+1)x^2=19^2
4x^2=19^2
x^2=(19^2)/4
x=((19^2)/4)^.5
x=9.5

Combine your like terms:

4x^2=19^2

Take the square root of both sides:

2x=19

Divide by 2.

x=9.5