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The solutions are \(x=-7\) and \(x=13\).
Solución
Solve the equation \( x^{2}=6x+91 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x^{2}=6x+91\)
- step1: Move the expression to the left side:
\(x^{2}-6x-91=0\)
- step2: Factor the expression:
\(\left(x-13\right)\left(x+7\right)=0\)
- step3: Separate into possible cases:
\(\begin{align}&x-13=0\\&x+7=0\end{align}\)
- step4: Solve the equation:
\(\begin{align}&x=13\\&x=-7\end{align}\)
- step5: Rewrite:
\(x_{1}=-7,x_{2}=13\)
The solutions to the equation \(x^{2}=6x+91\) are \(x=-7\) and \(x=13\).
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Bonus Knowledge
To solve the equation \( x^{2} = 6x + 91 \), start by rearranging it into standard quadratic form: \( x^{2} - 6x - 91 = 0 \). Now, you can apply the quadratic formula \( x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a} \). Here, \( a = 1, b = -6, \) and \( c = -91 \). This will give you two potential solutions for \( x \). After calculating the discriminant \( b^{2} - 4ac \), you’ll find it's a positive number, indicating that both solutions are real and distinct. Plug those values into the quadratic formula, and voilà—you'll have your solutions for \( x \)!
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