Question

Solve x2 – 8x = 3 by completing the square. Which is the solution set of the equation?

(4 minus StartRoot 19 EndRoot comma 4 + StartRoot 19 EndRoot)
(4 minus StartRoot 11 EndRoot comma 4 + StartRoot 11 EndRoot)
(4 minus StartRoot 8 EndRoot comma 4 + StartRoot 8 EndRoot)
(4 minus StartRoot 3 EndRoot comma 4 + StartRoot 3 EndRoot)

Answer 1

Answer:

x = 4 ± $\sqrt{19}$

Step-by-step explanation:

Given

x² - 8x = 3

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = 3 + 16

(x - 4)² = 19 ( take the square root of both sides )

x - 4 = ± $\sqrt{19}$ ( add 4 to both sides )

x = 4 ± $\sqrt{19}$, that is

x = 4 - $\sqrt{19}$, 4 + $\sqrt{19}$

Answer 2

The solution to the given quadratic equation using the completing the square method is x = ±√19 + 4

Completing the square method

Quadratic equations are equation that has a degree of 2

Given the quadratic equation expressed as x² – 8x = 3

In order to complete the square, we will follow the steps below;

Half of the coefficient of x = -8/2 .= -4

Square of the half of coefficient  =(-4)²

Add the result to both sides to have:

x² – 8x + (-4)² =3 + (-4)²

(x-4)² = 3 + 16

(x-4)² = 19

Take the square root of both sides

√(x-4)² = ±√19

x -4 = ±√19

x = ±√19 + 4

Hence the solution to the given quadratic equation using the completing the square method is x = ±√19 + 4

Learn more on completing the square here: https://brainly.com/question/13981588

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