What are the solutions to the equation (3/2 x-1/2)^2-0.8(1-x)=0 ?

The solutions to the equation (3/2 x-1/2)^2-0.8(1-x)=0 are x=(7+4sqrt(34))/(45),x=(7-4sqrt(34))/(45)

Find the zeros of (3/2 x-1/2)^2-0.8(1-x)=0

The zeros of (3/2 x-1/2)^2-0.8(1-x)=0 are x=(7+4sqrt(34))/(45),x=(7-4sqrt(34))/(45)

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(\frac{3}{2} x - \frac{1}{2})^{2} - 0.8 (1 - x) = 0

x = \frac{7 + 4 34}{45}, x = \frac{7 - 4 34}{45}

Decimal Notation

x = 0.67386 \dots, x = - 0.36275 \dots

Solution steps

(\frac{3}{2} x - \frac{1}{2})^{2} - 0.8 (1 - x) = 0

Multiply both sides by

10

10 (\frac{3}{2} x - \frac{1}{2})^{2} - 8 (1 - x) = 0

Expand

10 (\frac{3}{2} x - \frac{1}{2})^{2} - 8 (1 - x) : - \frac{11}{2} + \frac{45}{2} x^{2} - 7 x

- \frac{11}{2} + \frac{45}{2} x^{2} - 7 x = 0

Write in the standard form

a x^{2} + b x + c = 0

\frac{45 x ^{2}}{2} - 7 x - \frac{11}{2} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 7 ) \pm ( - 7 ) ^{2} - 4 \cdot \frac{45}{2} ( - \frac{11}{2} )}{2 \cdot \frac{45}{2}}

(- 7)^{2} - 4 \cdot \frac{45}{2} (- \frac{11}{2}) = 434

x_{1, 2} = \frac{- ( - 7 ) \pm 4 34}{2 \cdot \frac{45}{2}}

Separate the solutions

x_{1} = \frac{- ( - 7 ) + 4 34}{2 \cdot \frac{45}{2}}, x_{2} = \frac{- ( - 7 ) - 4 34}{2 \cdot \frac{45}{2}}

x = \frac{- ( - 7 ) + 4 34}{2 \frac{45}{2}} : \frac{7 + 4 34}{45}

x = \frac{- ( - 7 ) - 4 34}{2 \frac{45}{2}} : \frac{7 - 4 34}{45}

The solutions to the quadratic equation are:

x = \frac{7 + 4 34}{45}, x = \frac{7 - 4 34}{45}

(200 + 20 x) (40 - 2 x) = 9000

t = \frac{1}{2} \cdot (- 9.81) \cdot t^{2} + 20 \cdot t + 5

- 4 d^{2} - d + 3 = 0

40 x = - 1000 + 25 x + \frac{1}{2} (1.5) x^{2}

y = 3 x^{2} - 5 x - 4, x

What are the solutions to the equation (3/2 x-1/2)^2-0.8(1-x)=0 ?
The solutions to the equation (3/2 x-1/2)^2-0.8(1-x)=0 are x=(7+4sqrt(34))/(45),x=(7-4sqrt(34))/(45)
Find the zeros of (3/2 x-1/2)^2-0.8(1-x)=0
The zeros of (3/2 x-1/2)^2-0.8(1-x)=0 are x=(7+4sqrt(34))/(45),x=(7-4sqrt(34))/(45)