1) Solve the quadratic equation by completing the square. 6x2 + 4x - 5 = 0

Given the quadratic equation:

6x^2 + 4x - 5

a= 6

b =4

c = -5

Solve the quadratic equation:

Solution:

In order to solve for the roots of an equation, we simply must look at the 2nd and 3rd values. First, we must think of two numbers that when added, the answer is 4, and when multiplied, the answer is -5. 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 formula for the quadratic equation.

x = −b ± √(b^2 − 4ac)/2a
x = −4 ± √(4^2 − 4(6)(-5))/2(6)
x = −4 ± √(16 + 120)/12
x = −4 ± √(136)/12
x = −4 ± 11.66/12

Solve for + - separately.

x = -4 + 11.66/12
x = 0.64

x = -4 - 11.66/12
x = -1.305

Final answer:

x = 0.64

x = -1.305