FINDING UNKNOWN NUMBER
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Find the value of x given the equation:
- [tex]\boxed{\tt{ \textrm{-} x^{2} + 14x = 49}}[/tex]
[tex]\\[/tex]
[tex]\rm{\underline{SOLUTION:}}[/tex]
Rewrite the equation in quadratic form then multiply all terms by -1 to make the quadratic equation positive.
[tex]\\[/tex]
- [tex]\tt{ \textrm{-} x^{2} + 14x = 49}[/tex]
- [tex]\tt{\textrm{-}x^{2} + 14x - 49 = 0}[/tex]
- [tex]\tt{( \textrm{-}x^{2} \times \textrm{-}1) + (14x \times \textrm{-}1 )- (49 \times \textrm{-}1) = 0}[/tex]
- [tex]\tt{x^{2} - 14x + 49 = 0}[/tex]
- [tex]\tt{x^{2} - 2 \times x \times 7 + 7^{2} = 0}[/tex]
- [tex]\tt{(x-7)^{2} = 0}[/tex]
- [tex]\tt{(x-7) (x-7) = 0}[/tex]
- [tex]\tt{x = \green{7, \: 7}}[/tex]
[tex]\\[/tex]
The solution to the equation is 7, 7.
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[tex]\large{\boxed{\tt{\blue{06/13/2024}}}}[/tex]
