(m+4)(m-10)=0 solution:⬜m²-⬜m=0
Answers
Step-by-step explanation:
1
Distribute
(
+
4
)
(
−
1
0
)
=
0
{\color{#c92786}{(m+4)(m-10)}}=0
(
−
1
0
)
+
4
(
−
1
0
)
=
0
{\color{#c92786}{m(m-10)+4(m-10)}}=0
2
Distribute
(
−
1
0
)
+
4
(
−
1
0
)
=
0
{\color{#c92786}{m(m-10)}}+4(m-10)=0
2
−
1
0
+
4
(
−
1
0
)
=
0
{\color{#c92786}{m^{2}-10m}}+4(m-10)=0
3
Distribute
2
−
1
0
+
4
(
−
1
0
)
=
0
m^{2}-10m+{\color{#c92786}{4(m-10)}}=0
2
−
1
0
+
4
−
4
0
=
0
m^{2}-10m+{\color{#c92786}{4m-40}}=0
4
Combine like terms
2
−
1
0
+
4
−
4
0
=
0
m^{2}{\color{#c92786}{-10m}}+{\color{#c92786}{4m}}-40=0
2
−
6
−
4
0
=
0
m^{2}{\color{#c92786}{-6m}}-40=0
5
Use the quadratic formula
=
−
±
2
−
4
√
2
m=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
2
−
6
−
4
0
=
0
m^{2}-6m-40=0
=
1
a={\color{#c92786}{1}}
=
−
6
b={\color{#e8710a}{-6}}
=
−
4
0
c={\color{#129eaf}{-40}}
=
−
(
−
6
)
±
(
−
6
)
2
−
4
⋅
1
(
−
4
0
)
√
2
⋅
1
m=\frac{-({\color{#e8710a}{-6}}) \pm \sqrt{({\color{#e8710a}{-6}})^{2}-4 \cdot {\color{#c92786}{1}}({\color{#129eaf}{-40}})}}{2 \cdot {\color{#c92786}{1}}}
6
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Multiply the numbers
=
6
±
1
4
2
m=\frac{6 \pm 14}{2}
7
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
=
6
+
1
4
2
m=\frac{6+14}{2}
=
6
−
1
4
2
m=\frac{6-14}{2}
8
Solve
Rearrange and isolate the variable to find each solution
=
1
0
m=10
=
−
4
m=-4
Solution
=
1
0
=
−
4
m=10\\m=-4