Solve (x+5)² = 0: Finding the Parameter Value

Perfect Square Equations with Zero Property

Find the value of the parameter x.

(x+5)2=0 (x+5)^2=0

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Step-by-step video solution

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00:00 Solve
00:03 Extract root
00:10 Square root cancels square
00:14 Isolate the unknown
00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the value of the parameter x.

(x+5)2=0 (x+5)^2=0

2

Step-by-step solution

To solve the equation (x+5)2=0(x+5)^2 = 0, we will use the fact that a perfect square is zero only when the quantity being squared is zero itself.

  • Step 1: Set x+5=0 x+5 = 0 since it is the term being squared.
  • Step 2: Solve for x x by subtracting 5 from both sides: x+5=0 x+5 = 0 x=5 x = -5

Therefore, the solution to the equation is x=5 x = -5 .

3

Final Answer

x=5 x=-5

Key Points to Remember

Essential concepts to master this topic
  • Zero Property: A perfect square equals zero only when the base equals zero
  • Technique: Set x+5=0 x+5 = 0 and solve for x directly
  • Check: Substitute x = -5: (5+5)2=02=0 (-5+5)^2 = 0^2 = 0

Common Mistakes

Avoid these frequent errors
  • Taking the square root of both sides and getting ±0
    Don't write x+5=±0 x+5 = ±0 = x = -5 or x = -5! Since ±0 equals just 0, this creates confusion and doesn't change the answer. Always recognize that 0=0 \sqrt{0} = 0 only, so x+5=0 x+5 = 0 has just one solution.

Practice Quiz

Test your knowledge with interactive questions

Find the value of the parameter x.

\( 2x^2-7x+5=0 \)

FAQ

Everything you need to know about this question

Why don't I get two solutions like other quadratic equations?

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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.

Should I expand the squared term first?

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No need! Expanding (x+5)2 (x+5)^2 into x2+10x+25=0 x^2 + 10x + 25 = 0 makes it harder. Use the zero property directly: if something squared equals zero, that something must be zero.

What if the equation was (x+5)² = 4 instead?

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Then you would take the square root of both sides: x+5=±2 x+5 = ±2 , giving you two solutions: x = -3 and x = -7. But when the right side is zero, there's only one solution!

How is this different from regular quadratic equations?

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Most quadratics like x2+3x+2=0 x^2 + 3x + 2 = 0 have two different solutions. But perfect square equations that equal zero always have one repeated solution, making them special cases.

Can I check my answer a different way?

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Yes! Since (x+5)2 (x+5)^2 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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