Find the value of the parameter x.
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Find the value of the parameter x.
To solve the equation , we will use the fact that a perfect square is zero only when the quantity being squared is zero itself.
Therefore, the solution to the equation is .
Find the value of the parameter x.
\( 2x^2-7x+5=0 \)
This equation has a repeated root! When a perfect square equals zero, the expression inside must be zero, giving only one unique solution. It's technically a double root: x = -5 appears twice.
No need! Expanding into makes it harder. Use the zero property directly: if something squared equals zero, that something must be zero.
Then you would take the square root of both sides: , giving you two solutions: x = -3 and x = -7. But when the right side is zero, there's only one solution!
Most quadratics like have two different solutions. But perfect square equations that equal zero always have one repeated solution, making them special cases.
Yes! Since represents area of a square with side length |x+5|, when this area is zero, the side length must be zero too: |x+5| = 0, so x = -5.
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