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aguilerapablo03

x = ±2.12 - 2. Solving the quadratic equation 2x²+8x-1=0 by using completing the square, we obtain the roots x = 0.12 and x = -4.12.

We can solve the quadratic equation 2x²+8x-1=0 by completing the square follow the next steps:

Divide the coefficients of the equation by a (the coefficient x²)

(2x²+8x-1)/2=0 -----> x²+4x-1/2=0

Move the  independent term c/a to the right side of the equation

x²+4x = 1/2

Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation using (b/2)².

(b/2)²=(4/2)²=2²=4

x²+4x+4 = 1/2+4 -------> (x+2)² = 9/2

Applying square root on both sides of the equation

x+2 = √9/2

Finally, clear the x

x = √9/2 - 2 ----------> x = ±2.12132 - 2

Correct to 2 decimal places

x = ± 2.12 - 2

boffeemadrid

The equations is needed to be solved by completing the squares.

The values of [tex]x[/tex] are [tex]0.12,-4.12[/tex]

The equation is

[tex]2x^2+8x-1=0[/tex]

Dividing the equation by [tex]2[/tex]

[tex]x^2+4x-0.5=0\\\Rightarrow x^2+4x=0.5[/tex]

Finding [tex](\dfrac{b}{2})^2[/tex]

[tex](\dfrac{b}{2})^2=(\dfrac{4}{2})^2=4[/tex]

Adding it to the equation on both sides

[tex]x^2+4x+4=0.5+4\\\Rightarrow (x+2)^2=4.5\\\Rightarrow x+2=\pm\sqrt{4.5}\\\Rightarrow x=\sqrt{4.5}-2,-\sqrt{4.5}-2\\\Rightarrow x=0.12,-4.12[/tex]

The values of [tex]x[/tex] are [tex]0.12,-4.12[/tex]

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