Question

Use the quadratic formula to determine the solutions to the quadratic equation. Write your answers as decimals, and round to the nearest hundredth (2 decimal spots).

6x2+4x−3=0

Answer 1

Either x≈ -1.12 or x ≈0.45

Explanation:

Using the quadratic formula to solve this, we will follow the steps below;

First, write down the quadratic formula;

x = -b ±√b² - 4ac /2a

From the question, the equation given is: 6x²+4x−3=0

comparing the equation given withe standard equation ax² + bx + c=0

a= 6 b= 4 and c = -3

We can now proceed to insert the values into the formula;

x = -4 ±√4² - 4(6)(-3) /2(6)

x = -4 ±√16+72 /12

x = -4 ±√88 /12

Either x = -4+√88 /12

x ≈0.45

OR

x = -4 -√88 /12

x≈ -1.12

Either x≈ -1.12 or x ≈0.45

Answer 2

x1 = 0.45 and x2 = -1.12

Explanation:

To solve the equation 6x2+4x−3=0 using the quadratic formula, we use the following equation:

x = [-b ± √(b2 - 4ac)] / 2a

Where a, b and c are coefficients of the quadratic equantion (in our case, a = 6, b = 4 and c = -3)

So we have that:

x1 = [-4 + √(16 + 72)] / 12 = (-4 + 9.3808) / 12 = 0.4484

x2 = [-4 - √(16 + 72)] / 12 = (-4 - 9.3808) / 12 = -1.1151

Rounding to nearest hundredth, we have x1 = 0.45 and x2 = -1.12