factorise this expression completely with working
4(x+1)^2-49
Answers
Answer:
How to solve your question
Your question is
4
2
−
4
9
=
0
4x^{2}-49=0
4x2−49=0
Quadratic formula
Factor
1
Use the quadratic formula
=
−
±
2
−
4
√
2
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
4
2
−
4
9
=
0
4x^{2}-49=0
4x2−49=0
=
4
a={\color{#c92786}{4}}
a=4
=
0
b={\color{#e8710a}{0}}
b=0
=
−
4
9
c={\color{#129eaf}{-49}}
c=−49
=
−
0
±
0
2
−
4
⋅
4
(
−
4
9
)
√
2
⋅
4
x=\frac{-{\color{#e8710a}{0}} \pm \sqrt{{\color{#e8710a}{0}}^{2}-4 \cdot {\color{#c92786}{4}}({\color{#129eaf}{-49}})}}{2 \cdot {\color{#c92786}{4}}}
x=2⋅4−0±02−4⋅4(−49)
2
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(4*x-1)^2-(49)=0
Step by step solution :
STEP
1
:
1.1 Evaluate : (4x-1)2 = 16x2-8x+1
STEP
2
:
Pulling out like terms
2.1 Pull out like factors :
16x2 - 8x - 48 = 8 • (2x2 - x - 6)
Trying to factor by splitting the middle term
2.2 Factoring 2x2 - x - 6
The first term is, 2x2 its coefficient is 2 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 2 • -6 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -1 .
-12 + 1 = -11
-6 + 2 = -4
-4 + 3 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 3
2x2 - 4x + 3x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-2)
Add up the last 2 terms, pulling out common factors :
3 • (x-2)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (x-2)
Which is the desired factorization