The value of x for the quadratic equation is 1.099 or -9.099 .
What is completing the square?
Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial .
To solve ax²+bx+c=0 by completing the square:
1. Transform the equation so that the constant term, c , is alone on the right side.
2. If a , the leading coefficient (the coefficient of the x² term), is not equal to 1 , divide both sides by a .
3. Add the square of half the coefficient of the x -term, [tex](\frac{b}{2a} )^{2}[/tex] to both sides of the equation.
4. Factor the left side as the square of a binomial.
5. Take the square root of both sides. (Remember: (x+q)²=r is equivalent to x+q= ±√ r.)
6. Solve for x .
According to the question
Quadratic equation by completing the square
x² + 8x = 10
As we will try to make complete square of left side
for that
we have to add [tex](\frac{b}{2a} )^{2}[/tex] to both sides of the equation
As
a = 1
2ab = 8
b = 4
x² + 8x + 4² = 10 + 4²
By using the identity ( [tex](x+y)^{2} = x^{2} +y^{2} +2xy[/tex] )
(x + 4)² = 10 + 16
(x + 4)² = 26
x + 4 = ±[tex]\sqrt{26}[/tex]
x + 4 = ± 5.099
x = 5.099 - 4
x = 1.099
or
x = -5.099 - 4
x = -9.099
Hence, The value of x for the quadratic equation is 1.099 or -9.099 .
To know more about completing the square here:
https://brainly.com/question/4822356
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