Solve for x:
(2x + 3) (5 + x)=0
Answers
Step-by-step explanation:
1
Rearrange terms
(
2
+
3
)
(
5
+
)
=
0
(
2
+
3
)
(
+
5
)
=
0
2
Combine multiplied terms into a single fraction
(
2
+
3
)
(
+
5
)
=
0
(
+
5
)
2
+
3
=
0
3
Distribute
(
+
5
)
2
+
3
=
0
2
+
5
2
+
3
=
0
4
Multiply all terms by the same value to eliminate fraction denominators
2
+
5
2
+
3
=
0
(
2
+
3
)
(
2
+
5
2
+
3
)
=
0
5
Cancel multiplied terms that are in the denominator
(
2
+
3
)
(
2
+
5
2
+
3
)
=
0
2
+
5
=
0
6
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
+
5
=
0
x^{2}+5x=0
x2+5x=0
=
1
a={\color{#c92786}{1}}
a=1
=
5
b={\color{#e8710a}{5}}
b=5
=
0
c={\color{#129eaf}{0}}
c=0
=
−
5
±
5
2
−
4
⋅
1
⋅
0
√
2
⋅
1
7
Simplify
Evaluate the exponent
Multiply by zero
Add the numbers
Evaluate the square root
Multiply the numbers
=
−
5
±
5
2
8
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
=
−
5
+
5
2
=
−
5
−
5
2
9
Solve
Rearrange and isolate the variable to find each solution
=
0
=
−
5
Therefore :
Either
Or