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vazorg [7]
3 years ago
9

The steps to derive the quadratic formula are shown below: Step 1 ax2 + bx + c = 0 Step 2 ax2 + bx = − c Step 3 x2 + b over a ti

mes x equals negative c over a Step 4 x2 + b over a times x plus b squared over 4 times a squared equals negative c over a plus b squared over 4 times a squared Step 5 x2 + b over a times x plus b squared over 4 times a squared equals negative 4 multiplied by a multiplied by c, all over 4 multiplied by a squared plus b squared over 4 times a squared Step 6 Provide the next step to derive the quadratic formula. x plus b over 2 times a equals plus or minus b squared minus 4 times a times c all over the square root of 4 times a squared x plus b over 2 times a equals plus or minus b minus 2 times a times c all over square root of 2 times a x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 2 times a
Mathematics
1 answer:
Nostrana [21]3 years ago
3 0

Answer:

x + \frac{b}{2a} =  \frac{+/ -  \sqrt{b^2-4ac} }{2a}

Step-by-step explanation:

<u><em>Step 1:</em></u>

ax^2+bx+c = 0

<u><em>Step 2:</em></u>

ax^2+bx = -c

<u><em>Step 3:</em></u>

\frac{ax^2+bx}{a} = \frac{-c}{a}

<u><em>Step 4:</em></u>

Adding \frac{b^2}{4a^2} to both sides to complete the square

x^2 + \frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}

<u><em>Step 5:</em></u>

x^2 + \frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-4ac+b^2}{4a^2}

<u><em>Step 6:</em></u>

Taking square root on both sides

x + \frac{b}{2a} =  \frac{+/ -  \sqrt{b^2-4ac} }{2a}

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