Assignment: [tex]\bold{Solve \ Equation: \ x=\sqrt{13x-42}}[/tex]
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Answer: [tex]\boxed{\bold{x=7,\:x=6}}[/tex]
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Explanation: [tex]\downarrow\downarrow\downarrow[/tex]
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[ Step One ] Square Both Sides
[tex]\bold{x^2=\left(\sqrt{13x-42}\right)^2}[/tex]
[ Step Two ] Expand [tex]\bold{\left(\sqrt{13x-42}\right)^2}[/tex]
[tex]\bold{13x-42}[/tex]
[ Step Three ] Rewrite Equation
[tex]\bold{x^2=13x-42}[/tex]
[ Step Four ] Solve [tex]\bold{x^2=13x-42}[/tex]
[tex]\bold{x=7,\:x=6}[/tex]
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[tex]\bold{\rightarrow Mordancy \leftarrow}[/tex]
Answer:
x = 6, x = 7
Step-by-step explanation:
Given
x = [tex]\sqrt{13x-42}[/tex] ← square both sides
x² = 13x - 42 ← subtract 13x - 42 from both sides
x² - 13x + 42 = 0 ← in standard form
(x - 6)(x - 7) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x - 7 = 0 ⇒ x = 7
As a check substitute these values into the right side of the equation and if equal to the left side then they are the solutions
x = 6 : [tex]\sqrt{78-42}[/tex] = [tex]\sqrt{36}[/tex] = 6 ← solution
x = 7 : [tex]\sqrt{91-42}[/tex] = [tex]\sqrt{49}[/tex] = 7 ← solution
