Question

Solve the equation x2 - 16x + 54 = 0 by completing the square.
Fill in the values of a and b to complete the solutions.​

Answer 1

$\textbf{Given:}$

$\textsf{Equation is}\;\mathsf{x^2-16x+54=0}$

$\textbf{To find:}$

$\textsf{The solution of the given quadratic equation}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{x^2-16x+54=0}$

$\textsf{This can be written as}$

$\mathsf{x^2-16x=-54}$

$\textsf{Adding bothsides of the equation by 64}$

$\mathsf{x^2-16x+64=-54+64}$

$\mathsf{(x-8)^2=10}$

$\textsf{Taking square root,}$

$\mathsf{x-8=\pm\sqrt{10}}$

$\mathsf{x=8\pm\sqrt{10}}$

$\therefore\underline{\mathsf{The\;solution\;set\;is\;\{8+\sqrt{10},\;8-\sqrt{10}\}}}$

$\textbf{Answer:}$

$\textbf{a=8 and b=10}$

Find more:

Find the roots of the following quadratic (if they exist) by the method of completing the square.

2x²-7x+3=0

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