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# Solve using the quadratic formula 0.8x – 0.2×2 = -1

Solve using the quadratic formula 0.8x – 0.2x2 = -1

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

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