QuestionComplete the square on the following quadrat $x^{2}+4 x+24=0$

Studdy Solution

STEP 1

1. We are given a quadratic equation in the form $x^2 + bx + c = 0$ .
2. The goal is to rewrite the quadratic equation in the form $(x + d)^2 = e$ , where $d$ and $e$ are constants.
3. Completing the square involves creating a perfect square trinomial on one side of the equation.

STEP 2

1. Move the constant term to the other side of the equation.
2. Determine the value needed to complete the square.
3. Add and subtract this value inside the equation.
4. Rewrite the equation as a perfect square trinomial.
5. Simplify the equation.

STEP 3

Move the constant term to the other side of the equation:
$x^2 + 4x + 24 = 0$
Subtract 24 from both sides:
$x^2 + 4x = -24$

STEP 4

Determine the value needed to complete the square. Take half of the coefficient of $x$ , which is 4, and square it:
$\left(\frac{4}{2}\right)^2 = 2^2 = 4$

STEP 5

Add and subtract this value (4) inside the equation:
$x^2 + 4x + 4 - 4 = -24$
This can be rewritten as:
$(x^2 + 4x + 4) - 4 = -24$

STEP 6

Rewrite the equation as a perfect square trinomial:
$(x + 2)^2 - 4 = -24$

STEP 7

Simplify the equation by adding 4 to both sides:
$(x + 2)^2 = -24 + 4$
$(x + 2)^2 = -20$
The completed square form of the equation is:
$(x + 2)^2 = -20$

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