Use algebraic strategies to solve √2x+3=x . How many solutions did you come up with? Which strategies did you use?

Given:

√2x+3=x .

Determine the solutions.

Solution:

In order to  determine the solutions, we simply need to solve for x. The first step is to square both sides of the equation to cancel out the square root sign.

√2x+3 = x 

(√2x+3 )^2= (x)^2

2x + 9 = x^2

Transpose 2x and 9 to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.

= x^2 - 2x - 9

a = x

b = -2

c= -9

In order to solve for the roots or solutions of a quadratic equation, we simply must look at the 2nd and 3rd value. First we must think of two numbers that when added, the answer is -2, and when multiplied, the answer is -9. Hence, if we are unable to find the number, we will use the quadratic formula.

The Quadratic formula:

x = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number.

Substitute the given values of a, b and c to the quadratic formula.

x = −b ± √(b^2 − 4ac)/2a

x = −(-2) ± √((-2)^2 − 4(1)(-9))/2(1)

x = 2 ± √(4 + 36)/2

x = 2 ± √(40)/2

x = 2 ± 6.32/2

Solve for +- separately.

x = 2 + 6.32/2
x = 8.32/2
x = 4.16

x = 2 - 6.32/2
x = -2.16

Final answer:
x = 4.16
x = -2.16