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The solutions are \(x=-10\) and \(x=-8\).
Solución
Solve the equation \( x^{2}+18x+81=1 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x^{2}+18x+81=1\)
- step1: Move the expression to the left side:
\(x^{2}+18x+80=0\)
- step2: Factor the expression:
\(\left(x+8\right)\left(x+10\right)=0\)
- step3: Separate into possible cases:
\(\begin{align}&x+8=0\\&x+10=0\end{align}\)
- step4: Solve the equation:
\(\begin{align}&x=-8\\&x=-10\end{align}\)
- step5: Rewrite:
\(x_{1}=-10,x_{2}=-8\)
The solutions to the equation \(x^{2}+18x+81=1\) are \(x=-10\) and \(x=-8\).
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Simplifique esta solución Extra Insights
To solve the equation \( x^{2}+18 x+81=1 \), you first want to move the '1' to the left side to set the equation to zero: \( x^{2} + 18x + 81 - 1 = 0 \) which simplifies to \( x^{2} + 18x + 80 = 0 \). Now you can factor the quadratic. You're looking for two numbers that multiply to 80 and add to 18. Those numbers are 10 and 8. So, the factored form is: \( (x + 10)(x + 8) = 0 \). Setting each factor to zero gives you the solutions: \( x + 10 = 0 \) or \( x + 8 = 0 \), leading to \( x = -10 \) and \( x = -8 \). Thus, the final solutions for \( x \) are \( -10 \) and \( -8 \).
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