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Damm [24]
3 years ago
6

In the derivation of the quadratic formula by completing the square, the equation (x+b over 2a)^2=-4ac+b^2 over 4a^2 is created

by forming a perfect square trinomial. What is the result of applying the square root property of equality to this equation?
Mathematics
2 answers:
vredina [299]3 years ago
4 0

Answer:

The result of applying the square root property of equality to this equation is x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}.

Step-by-step explanation:

Consider the provided equation.

\left(x+\dfrac{b}{2a}\right)^2=\dfrac{-4ac+b^2}{4a^2}

As the above equation is formed by perfect square trinomial so simply applying the square root property as shown:

\sqrt{(x+\dfrac{b}{2a})^2}=\pm \dfrac{\sqrt{-4ac+b^2}}{\sqrt{4a^2}}\\x+\dfrac{b}{2a}=\pm \dfrac{\sqrt{b^2-4ac}}{2a}

Isolate the variable x.

x=-\dfrac{b}{2a}\pm \dfrac{\sqrt{b^2-4ac}}{2a}\\x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

Hence, the result of applying the square root property of equality to this equation is x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}.

Alja [10]3 years ago
3 0

Answer:

x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

Step-by-step explanation:

The given equation is

(x+\dfrac{b}{2a})^2=\dfrac{-4ac+b^2}{4a^2}

In the derivation of the quadratic formula by completing the square, the above equation is created by forming a perfect square trinomial.

Applying the square root property of equality to this equation, we get

\sqrt{(x+\dfrac{b}{2a})^2}=\pm \sqrt{\dfrac{-4ac+b^2}{4a^2}}

x+\dfrac{b}{2a}=\pm \dfrac{\sqrt{-4ac+b^2}}{\sqrt{4a^2}}

x+\dfrac{b}{2a}=\pm \dfrac{\sqrt{b^2-4ac}}{2a}

Subtract \frac{b}{2a} from both sides.

x+\dfrac{b}{2a}-\dfrac{b}{2a}=\pm \dfrac{\sqrt{b^2-4ac}}{2a}-\dfrac{b}{2a}

x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

Therefore, the required equation is x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}.

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The model which model the dimensions of the bed has been attached.

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<h3>What is the perimeter and area of the bed?</h3>

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Step-by-step explanation:

You can do it by elaborating :

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= 8.00 + 1.6 + 0.12

= 9.72

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