JanimahmaIuntawanidn
Answered

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-X^2 + 14x = 49
X = ?​

Sagot :

NoahBadillaidn

FINDING UNKNOWN NUMBER

[tex]\normalsize{\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}}}[/tex]

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.

[tex]\normalsize{\blue{\overline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}}}[/tex]

[tex]\large{\boxed{\tt{\blue{06/13/2024}}}}[/tex]

Answer:

x = 7

Step-by-step explanation:

[tex] {x}^{2} + 14x - 49 = 0[/tex]

[tex] {x}^{2} - 14x + 49 = 0[/tex]

[tex] {( x- 7})^{2} [/tex]

[tex]x - 7 = 0[/tex]

[tex]x = 7[/tex]

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