Question

14 - 3x² = -418
-15 + 6y² = 471
show your
work!!!!!!!!!!!!!!!!!!!
x =

y =

now double your two
answers and find the sum
answer =

Explanation:

Step1: Isolate $x^2$ term

Subtract 14 from both sides:
$14 - 3x^2 - 14 = -418 - 14$
$-3x^2 = -432$

Step2: Solve for $x^2$

Divide by -3:
$\frac{-3x^2}{-3} = \frac{-432}{-3}$
$x^2 = 144$

Step3: Solve for $x$

Take square root:
$x = \pm\sqrt{144} = \pm12$

Step4: Isolate $y^2$ term

Add 15 to both sides:
$-15 + 6y^2 + 15 = 471 + 15$
$6y^2 = 486$

Step5: Solve for $y^2$

Divide by 6:
$\frac{6y^2}{6} = \frac{486}{6}$
$y^2 = 81$

Step6: Solve for $y$

Take square root:
$y = \pm\sqrt{81} = \pm9$

Step7: Double values, find sums

Case 1: $x=12, y=9$: $2(12)+2(9)=24+18=42$
Case 2: $x=12, y=-9$: $2(12)+2(-9)=24-18=6$
Case 3: $x=-12, y=9$: $2(-12)+2(9)=-24+18=-6$
Case 4: $x=-12, y=-9$: $2(-12)+2(-9)=-24-18=-42$

Answer:

$x = \pm12$
$y = \pm9$