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Solve each equation by completing the square
z-5=z^2-25
after completing the equation, the equation is __ and the solution is ____
WHOEVER ANSWERS CORRECTLY AND FIRST WILL BE MARKED AS BRAINLIEST

Respuesta :

The equation becomes z + 5 = 1 and the value of the z in the given equation by completing the square is z = -4.

What is the equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given equation,

z - 5 = z² - 25

z - 5 = z² - 5²

By property that A² - B² = (A + B)(A - B)

z - 5 = (z - 5)(z + 5)

z + 5 = 1    

z = - 1 / 5 = - 4

Hence "By completing the square, the equation is changed to z + 5 = 1, and the value of z in the given equation is changed to z = -4".

For more about the equation,

brainly.com/question/10413253

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mhanifa

Answer:

  • The equation after completing the square is (z - 1/2)² = (9/2)²;
  • The solution is z = {-4; 5}

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Given equation:

  • z - 5 = z² - 25

Solve it as follows:

  • z - 5 = z² - 25                                          Given
  • z² - 25 - z + 5 = 0                                    Bring all terms to one side
  • z² - z - 20 = 0                                          Simplify
  • z² - 2*z*1/2 + (1/2)² = 20 + (1/2)²              Complete the square on left
  • (z - 1/2)² = 20 1/4                                    
  • (z - 1/2)² = 81/4                                         Square on the right
  • (z - 1/2)² = (9/2)²                                       Square root both sides
  • z - 1/2 = 9/2 and z - 1/2 = - 9/2
  • z = 1/2 + 9/2 and z = 1/2 - 9/2
  • z = 10/2 and z = - 8/2
  • z = 5 and z = - 4                                       Answer

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