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1) Solve the following quadritic equations by completing the square: i) X ² + 12x + = 15t 2 (i) x ~ 14x + 36=0

1) Solve the following quadritic equations by completing the square: i) X ² + 12x-example-1

1 Answer

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EXPLANATION

Filling the equation give us the following expression:

x^2 -14x + 36 = 0

Applying the square root relationship:


x_1,x_2=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}

Where a=1, b=-14, c=36

Replacing terms:


x_1,x_2=\frac{-(-14)\pm\sqrt[]{(14)^2-4\cdot1\cdot36}}{2\cdot1}

Multiplying numbers:


x_1,x_2=\frac{14\pm\sqrt[]{196-144}}{2}

Subtracting numbers:


x_1,x_2=\frac{14\pm\sqrt[]{52}}{2}

Solving the square root:


x_(1,)x_2=\frac{14\pm2\sqrt[]{13}}{2}

The solutions are:


x_1=\frac{14+2\sqrt[]{13}}{2}=7+\sqrt[]{13}
x_2=7-\sqrt[]{13}

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