**Solve using the quadratic formula 0.8x – 0.2x ^{2 }= -1**

## Answer

**x = 5, -1**

## Solution

**0.8x – 0.2x² = -1**

**Add 1 to both sides of the equation**

0.8x – 0.2x²+1=0

**Use the quadratic formula to find the solutions**

-b ± √b²- 4(ac) ÷ 2a

**Substitute the values a= -0.2, b=0.8, and c=1 into the quadratic formula and solve for x**

x = -0.8 ± √0.8² – 4(-0.2 X 1) ÷ 2(-0.2)

**Simplify the numerator by raising 0.8 to the power of 2**

x= -0.8 ± √0.64 – 4(-0.2) ÷ 2(-0.2)

**Multiply -4 by (-0.2) and 2 by (-0.2)**

x= -0.8 ± √0.64 +0.8 ÷ -0.4

**Add 0.64 and 0.8**

x = -0.8 ± √1.44 ÷ -0.4

**Rewrite 1.44 as 1.2²**

x = -0.8 ± √1.2² ÷ -0.4

**Pull terms out from under the radical, assuming positive real numbers**

x = -0.8 ± 1.2 ÷ -0.4

**Multiply both numerator and denominator by – 1**

x = -1(-0.8 ± 1.2) ÷ -0.4 X -1

x = 1(0.8 ± 1.2) ÷ 0.4

**Factor 0.4 out of 0.4**

x = 1(0.8 ± 1.2) ÷ 0.4(1)

**Separate the fractions**

x=1/0.4 and x = 0.8 ± 1.2/1

**Divide 1 by 0.4**

x=2.5(0.8 ± 1.2/1)

**Divide 0.8 ± 1.2 by 1**

x = 2.5(0.8 ± 1.2)

x = 2.5(0.8 + 1.2) or x = 2.5(0.8 – 1.2)

**Simplify x = 2.5(0.8 + 1.2) and x = 2.5(0.8 – 1.2)**

For x = 2.5(0.8 + 1.2), we have

x = 2.5 X 0.8 + 2.5 X 1.2

x = 2 + 3

x = 5

For x = 2.5(0.8 – 1.2), we have

x = 2.5 X 0.8 – 2.5 X 1.2

x = 2 – 3

x = -1

The final answer is the combination of both solutions

x = 5 or x = -1

**x=5, -1**