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Chapter 9: Q.175 (page 906)

In the following exercises, solve equations in Quadratic Form for 6x + x − 2 = 0.

Short Answer

Expert verified

The solution of the quadratic equation is x=14.

Step by step solution

01

Step 1. Given Information.

The given equation is 6x + x − 2 = 0.

02

Step 2. Remove Square root

Solving 6x + x − 2 = 0

6x − 2 = x

Squaring both sides , we get:-

(6x-2)2=(x)236x2-24x+4=x

03

Step 3. Solving using Quadratic equation.

Solving 36x2-24x+4=x

Subtracting x from both sides ,we get:-

36x2-24x+4-x=x-x36x2-25x+4=0

04

Step 4. Solve using quadratic formula

Solving 36x2-25x+4=0

x1, 2=--25±-252-4· 36· 42· 36x1, 2=--25± 72· 36x1=--25+72· 36, x2=--25-72· 36x=49, x=14

05

. Verifying the solution

Plug the value of x=14in equation 6x + x − 2 = 0, we get:-

614+14-2=32+12-232+12-2=0

Similarly , Plug the value of x=49in the equation, we get:-

6x + x − 2 =649+49-2649+49-2=83+23-283+23-2=103-2103-2=43

Since, 43≠0, Therefore, 43is not the solution of the equation. Hence, The solution is x=14.

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