The solution of the quadratic
equation.
x² - 20x - 44 = 0 is __________.
Answers
Answer:
(x + 2)(x - 22)
Step-by-step explanation:
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Step-by-step explanation:
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.
2
−
2
0
−
4
4
=
0
x^{2}-20x-44=0
x2−20x−44=0
=
1
a={\color{#c92786}{1}}
a=1
=
−
2
0
b={\color{#e8710a}{-20}}
b=−20
=
−
4
4
c={\color{#129eaf}{-44}}
c=−44
=
−
(
−
2
0
)
±
(
−
2
0
)
2
−
4
⋅
1
(
−
4
4
)
√
2
⋅
1
x=\frac{-({\color{#e8710a}{-20}}) \pm \sqrt{({\color{#e8710a}{-20}})^{2}-4 \cdot {\color{#c92786}{1}}({\color{#129eaf}{-44}})}}{2 \cdot {\color{#c92786}{1}}}
x=2⋅1−(−20)±(−20)2−4⋅1(−44)
2
Simplify
Evaluate the exponent
Multiply the numbers
=
2
0
±
4
0
0
−
4
⋅
1
(
−
4
4
)
√
2
⋅
1
x=\frac{20 \pm \sqrt{400{\color{#c92786}{-4}} \cdot {\color{#c92786}{1}}({\color{#c92786}{-44}})}}{2 \cdot 1}
x=2⋅120±400−4⋅1(−44)
=
2
0
±
4
0
0
+
1
7
6
√
2
⋅
1
x=\frac{20 \pm \sqrt{400+{\color{#c92786}{176}}}}{2 \cdot 1}
x=2⋅120±400+176
Add the numbers
Evaluate the square root
Multiply the numbers
=
2
0
±
2
4
2
x=\frac{20 \pm 24}{2}
x=220±24
3
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
=
2
0
+
2
4
2
x=\frac{20+24}{2}
x=220+24
=
2
0
−
2
4
2
x=\frac{20-24}{2}
x=220−24
4
Solve
Rearrange and isolate the variable to find each solution
=
2
2
x=22
x=22
=
−
2
x=-2
x=−2
Solution
=
2
2
=
−
2