Answer:
x = ±4
Step-by-step explanation:
Step 1: Write out quadratic
2x² - 5 = 27
Step 2: Add 5 to both sides
2x² = 32
Step 3: Divide both sides by 2
x² = 16
Step 4: Take the square root of both sides
x = ±4
∴ x can equal -4 or 4
Answer:
[tex] \boxed{ \bf \huge \: x =4}[/tex]
[tex] \rm \: Or,[/tex]
[tex] \boxed{\bf \huge \: x = - 4}[/tex]
Step by step explanation:
Given Equation is :-
[tex]\sf \implies \: 2 {x}^{2} - 5 = 27[/tex]
We need to find the value of [tex]x[/tex] using Quadric formula.
Firstly, Subtract 27 from both of the side(s):-
[tex]\sf \implies2 {x}^{2} - 5 - 27 = 27 - 27[/tex]
On Simplification:-
Add -5-27 as (-) and (-) equals to (+). -5-27 would be represented as 5+27, which results to 32.
[tex]\sf\sf \implies2 {x}^{2} - 32 = 0[/tex]
Then, for this equation , a=2, b=0, c=-32.
Put the values :-
That is,
[tex]\sf \implies2 {x}^{2} + 0x + ( - 32) = 0[/tex]
As we know, that the quadratic formula is:-
[tex]\sf \implies \: x = \dfrac{ -b \pm \sqrt{b {}^{2} - 4ac } }{2a} [/tex]
Put the values :-
[tex]\sf \implies \: x = \dfrac{ - 0 \pm \sqrt{0 {}^{2} \: - 4(2) ( - 32)} }{2(2)} [/tex]
On Simplification:-
[tex]\sf \implies \: x = \dfrac{ - 0 {}^{} \pm \sqrt{ {0 } - \: 8 \times - 32}}{2 \times 2} [/tex]
[tex]\sf \implies \: x = \dfrac{ - 0 \pm \: \sqrt{ - 8 \times - 32} }{4}[/tex]
[tex]\sf \implies x = \dfrac{ - {0}^{}\pm \: \sqrt{ + 256} }{4} [/tex]
As 0 has no value here,
[tex]\sf \implies \: x = \dfrac{ \pm \sqrt{256} }{4} [/tex]
On cancelling,
Remove the square of 256 ( √256)
[tex]\sf \implies \: x = \dfrac{ \pm \cancel{ \: 256}}{ \cancel4} [/tex]
[tex]\sf \implies \: x = ± + 4[/tex]
It may be represented as,
[tex]\sf \implies \: x = - 4[/tex]
Or,
[tex]\sf \implies \: x = 4[/tex]
_______________________________
I hope this helps!
Please let me know if you have any questions.
~MisterBrian
