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Answer
The solutions are \(x=-5\) and \(x=7\).
Solution
Solve the equation \( x(x-2)=35 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x\left(x-2\right)=35\)
- step1: Expand the expression:
\(x^{2}-2x=35\)
- step2: Move the expression to the left side:
\(x^{2}-2x-35=0\)
- step3: Factor the expression:
\(\left(x-7\right)\left(x+5\right)=0\)
- step4: Separate into possible cases:
\(\begin{align}&x-7=0\\&x+5=0\end{align}\)
- step5: Solve the equation:
\(\begin{align}&x=7\\&x=-5\end{align}\)
- step6: Rewrite:
\(x_{1}=-5,x_{2}=7\)
The solutions to the equation \(x(x-2)=35\) are \(x=-5\) and \(x=7\).
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Simplify this solution Mind Expander
To solve the equation \( x(x-2)=35 \), first, we rearrange it to form a standard quadratic equation: \( x^2 - 2x - 35 = 0 \). You can use the quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = -2 \), and \( c = -35 \). Plugging those values in gives you the solutions for \( x \). Once you find the roots, you can verify them by substituting back into the original equation to confirm they're correct. Remember, double-checking your steps helps avoid simple arithmetic errors.
