Question

Solve this equation for x: 2x^2 + 12x - 7 = 0

What is the first step to solve this equation?

-combine like terms

-factor the trinomial

-isolate the constant term by adding 7 to both sides

Answer 1

Explanation:

Step 1: Isolate the constant term by adding 7 to both sides of the equation.

Step 2: Factor 2 from the binomial.

Step 3: 9

Step 3 b: 18

Step4: write the trinomial as the square root of a binomial.

Step 5: divide both sides of the equation by 2 Step

6: Apply the square root property of equality Step

7: subtract 3 from both sides of the equation.

Answer 2

x=0.5355 or x=-6.5355

First step is to: Isolate the constant term by adding 7 to both sides

Explanation:

We want to solve this equation:
`2x^2 + 12x - 7 = 0`

On observation, the trinomial is not factorizable so we use the Completing the square method.

Step 1: Isolate the constant term by adding 7 to both sides

`2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7`

Step 2: Divide the equation all through by the coefficient of
`x^2` which is 2.

`x^2 + 6x=(7)/(2)`

Step 3: Divide the coefficient of x by 2, square it and add it to both sides.

Coefficient of x=6

Divided by 2=3

Square of 3=
`3^2`

Therefore, we have:

`x^2 + 6x+3^2=(7)/(2)+3^2`

Step 4: Write the Left Hand side in the form
`(x+k)^2`

`(x+3)^2=(7)/(2)+3^2\\(x+3)^2=12.5\\`

Step 5: Take the square root of both sides and solve for x

`x+3=\pm√(12.5)\\x=-3\pm √(12.5)\\x=-3+ √(12.5), $ or $x= -3- √(12.5)\\$x=0.5355 or x=-6.5355`