Solve by Completing the Square 24=x^2-4x+3

$24 = x^{2} - 4 x + 3$

Simplify the equation into a proper form to complete the square.

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$x^{2} - 4 x + 3 = 24$

Move all terms not containing $x$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$x^{2} - 4 x = 24 - 3$

Subtract $3$ from $24$ .

$x^{2} - 4 x = 21$

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(- 2)}^{2}$

Add the term to each side of the equation.

$x^{2} - 4 x + {(- 2)}^{2} = 21 + {(- 2)}^{2}$

Simplify the equation.

Simplify the left side.

Raise $- 2$ to the power of $2$ .

$x^{2} - 4 x + 4 = 21 + {(- 2)}^{2}$

Simplify the right side.

Simplify $21 + {(- 2)}^{2}$ .

Raise $- 2$ to the power of $2$ .

$x^{2} - 4 x + 4 = 21 + 4$

Add $21$ and $4$ .

$x^{2} - 4 x + 4 = 25$

Factor the perfect trinomial square into ${(x - 2)}^{2}$ .

${(x - 2)}^{2} = 25$

Solve the equation for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x - 2 = \pm \sqrt{25}$

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$x - 2 = \pm \sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x - 2 = \pm 5$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x - 2 = 5$

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$x = 5 + 2$

Add $5$ and $2$ .

$x = 7$

Next, use the negative value of the $\pm$ to find the second solution.

$x - 2 = - 5$

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$x = - 5 + 2$

Add $- 5$ and $2$ .

$x = - 3$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 7, - 3$

Solve by Completing the Square 24=x^2-4x+3

Related Questions

Support LCMGCF.com by disabling your adblocker.