The given quadratic equation can be represented in the form \((x-p)^2 = q\)
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
\(ax^2 + bx + c = 0\)
where \(a
eq 0\).
The given quadratic equation is
\(x^2 - 8x + 13 = 0\)
Case 1: Subtract 5 from both sides of the equation
i.e. \(x^2 - 8x + 13 - 5 = 0 - 5\)
⇒ \(x^2 - 8x + 8 = -5\)
The LHS of the above equation can not be expressed in \((x-p)^2\) form. Hence, it is not the correct step.
Case 2: Add 3 to both sides of the equation.
i.e. \(x^2 - 8x + 13 +3 = 0 + 3\)
⇒ \(x^2 - 8x + 16 = 3\)
⇒ \(x^2 - 2\times x \times 4 + (4)^2 =3\)
⇒ \((x - 4)^2 = 3\)
The above equation is expressed in \((x-p)^2 = q\) form where p = 4 and q = 3.
Case 3: Add 5 to both sides of the equation
i.e. \(x^2 - 8x + 13 + 5 = 0+5\)
⇒ \(x^2 - 8x + 18 = 5\)
The LHS of the above equation can not be expressed in the \((x-p)^2\). Hence, it is not the correct step.
Case 4: Subtract 3 from both sides of the equation
i.e. \(x^2 - 8x + 13 - 3 = 0-3\)
⇒ \(x^2 - 8x + 10 = -3\)
The LHS of the above equation can not be expressed in the \((x-p)^2\). Hence, it is not the correct step.
Hence, "Add 3 to both sides of the equation" is the correct step.
Learn more about quadratic equations here:
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