The given quadratic equation can be represented in the form [tex](x-p)^2 = q[/tex]
by adding 3 to both sides of the equation.
What is a quadratic equation?
The polynomial equation whose highest degree is two is called a quadratic equation. The equation is given by
[tex]ax^2 + bx + c = 0[/tex]
where [tex]a\neq 0[/tex].
The given quadratic equation is
[tex]x^2 - 8x + 13 = 0[/tex]
Case 1: Subtract 5 from both sides of the equation
i.e. [tex]x^2 - 8x + 13 - 5 = 0 - 5[/tex]
⇒ [tex]x^2 - 8x + 8 = -5[/tex]
The LHS of the above equation can not be expressed in [tex](x-p)^2[/tex] form. Hence, it is not the correct step.
Case 2: Add 3 to both sides of the equation.
i.e. [tex]x^2 - 8x + 13 +3 = 0 + 3[/tex]
⇒ [tex]x^2 - 8x + 16 = 3[/tex]
⇒ [tex]x^2 - 2\times x \times 4 + (4)^2 =3[/tex]
⇒ [tex](x - 4)^2 = 3[/tex]
The above equation is expressed in [tex](x-p)^2 = q[/tex] form where p = 4 and q = 3.
Case 3: Add 5 to both sides of the equation
i.e. [tex]x^2 - 8x + 13 + 5 = 0+5[/tex]
⇒ [tex]x^2 - 8x + 18 = 5[/tex]
The LHS of the above equation can not be expressed in the [tex](x-p)^2[/tex]. Hence, it is not the correct step.
Case 4: Subtract 3 from both sides of the equation
i.e. [tex]x^2 - 8x + 13 - 3 = 0-3[/tex]
⇒ [tex]x^2 - 8x + 10 = -3[/tex]
The LHS of the above equation can not be expressed in the [tex](x-p)^2[/tex]. Hence, it is not the correct step.
Hence, "Add 3 to both sides of the equation" is the correct step.
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