What are the solutions to the equation -(x-3)=(x-7/2)(x+3/4) ?

The solutions to the equation -(x-3)=(x-7/2)(x+3/4) are x=(7+sqrt(409))/8 ,x=(7-sqrt(409))/8

Find the zeros of -(x-3)=(x-7/2)(x+3/4)

The zeros of -(x-3)=(x-7/2)(x+3/4) are x=(7+sqrt(409))/8 ,x=(7-sqrt(409))/8

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- (x - 3) = (x - \frac{7}{2}) (x + \frac{3}{4})

x = \frac{7 + 409}{8}, x = \frac{7 - 409}{8}

Decimal Notation

x = 3.40296 \dots, x = - 1.65296 \dots

Solution steps

- (x - 3) = (x - \frac{7}{2}) (x + \frac{3}{4})

Expand

- (x - 3) : - x + 3

Expand

(x - \frac{7}{2}) (x + \frac{3}{4}) : x^{2} - \frac{11}{4} x - \frac{21}{8}

- x + 3 = x^{2} - \frac{11}{4} x - \frac{21}{8}

Switch sides

x^{2} - \frac{11}{4} x - \frac{21}{8} = - x + 3

Move

3

to the left side

- \frac{45}{8} - \frac{11}{4} x + x^{2} = - x

Move

x

to the left side

x^{2} - \frac{7}{4} x - \frac{45}{8} = 0

Write in the standard form

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

x^{2} - \frac{7 x}{4} - \frac{45}{8} = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - \frac{7}{4} ) \pm ( - \frac{7}{4} ) ^{2} - 4 \cdot 1 \cdot ( - \frac{45}{8} )}{2 \cdot 1}

(- \frac{7}{4})^{2} - 4 \cdot 1 \cdot (- \frac{45}{8}) = \frac{409}{4}

x_{1, 2} = \frac{- ( - \frac{7}{4} ) \pm \frac{409}{4}}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - \frac{7}{4} ) + \frac{409}{4}}{2 \cdot 1}, x_{2} = \frac{- ( - \frac{7}{4} ) - \frac{409}{4}}{2 \cdot 1}

x = \frac{- ( - \frac{7}{4} ) + \frac{409}{4}}{2 \cdot 1} : \frac{7 + 409}{8}

x = \frac{- ( - \frac{7}{4} ) - \frac{409}{4}}{2 \cdot 1} : \frac{7 - 409}{8}

The solutions to the quadratic equation are:

x = \frac{7 + 409}{8}, x = \frac{7 - 409}{8}

4 x^{2} - 13 x - 35 = 0

x, (x^{2} + y^{2} - 1) = x^{2} y^{3}

x, t (x) = 18 - 24 x + 2 x^{2}

9 x^{2} - 50 x + 57 = 0

- x^{2} + 1 = x - 1

What are the solutions to the equation -(x-3)=(x-7/2)(x+3/4) ?
The solutions to the equation -(x-3)=(x-7/2)(x+3/4) are x=(7+sqrt(409))/8 ,x=(7-sqrt(409))/8
Find the zeros of -(x-3)=(x-7/2)(x+3/4)
The zeros of -(x-3)=(x-7/2)(x+3/4) are x=(7+sqrt(409))/8 ,x=(7-sqrt(409))/8