elvishwitchxyp

2021-12-20

What is the answer to this quadratic:
$0=-2{a}^{2}±2b-12$
$-2{a}^{2}+2b-12=0$

### Answer & Explanation

censoratojk

Step 1
$2{a}^{2}+2b-12=0$ is not a solvable quadratic. I will assume you meant
$2{x}^{2}+2x-12$
The quadratic formula is:
$\frac{-b±\sqrt{{b}^{2}-\left(4ac\right)}}{2a}$
$\frac{-2±\sqrt{{2}^{2}-\left(4×2-12\right)}}{2×2}$
$\frac{-2±\sqrt{4-\left(-96\right)}}{4}$
$\frac{-2±\sqrt{100}}{4}$
$\frac{-2±10}{4}$
$\frac{12}{4}$ or $\frac{8}{4}$
The answer is $x=3$ or $x=2$

Navreaiw

Step 1
Given equation: $2{a}^{2}+2b-12=0$
Quadratic equations like this one, with an ${x}^{2}$ term but no x term, can still be solved using the quadratic formula, $\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$, once they are put in standard form: $a{x}^{2}+bx+c=0$
This equation is in standard form: $a{x}^{2}+bx+c=0$
Substitute 2 for a, 0 fro b, and $-12+2b$ for c in the quadratic formula, $\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$
$a=\frac{0±\sqrt{{0}^{2}-4×2\left(2b-12\right)}}{2×2}$
Square 0
$a=\frac{0±\sqrt{-4×2\left(2b-12\right)}}{2×2}$
Multiply -4 times 2
$a=\frac{0±\sqrt{-8\left(2b-12\right)}}{2×2}$
Multiply -8 times $-12+2b$
$a=\frac{0±\sqrt{96-16b}}{2×2}$
Take the square root of $96-16b$
$a=\frac{0±4\sqrt{6-b}}{2×2}$
Multiply 2 times 2
$a=\frac{0±4\sqrt{6-b}}{4}$
Now solve the equation $a=\frac{0±4\sqrt{6-b}}{4}$ when $±$ is plus and minus
$a=\sqrt{6-b}$
$a=-\sqrt{6-b}$

RizerMix

Step 1
$2{a}^{2}+2b-12=0$
Subtract $2{a}^{2}$ from both sides. Anything subtracted from zero gives its negation.
$2b-12=-2{a}^{2}$
Add 12 to both sides
$2b=-2{a}^{2}+12$
The equation is in standard form.
$2b=12-2{a}^{2}$
Divide both sides by 2
$\frac{2b}{2}=\frac{12-2{a}^{2}}{2}$
Dividing by 2 undoes the multiplication by 2.
$b=\frac{12-2{a}^{2}}{2}$
Divide $-2{a}^{2}+12$ by 2
$b=6-{a}^{2}$

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