What are the solutions to the equation -x^3+6x^2-7x=4 ?

The solutions to the equation -x^3+6x^2-7x=4 are x=4,x=1+sqrt(2),x=1-sqrt(2)

Find the zeros of -x^3+6x^2-7x=4

The zeros of -x^3+6x^2-7x=4 are x=4,x=1+sqrt(2),x=1-sqrt(2)

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- x^{3} + 6 x^{2} - 7 x = 4

x = 4, x = 1 + 2, x = 1 - 2

Decimal Notation

x = 4, x = 2.41421 \dots, x = - 0.41421 \dots

Solution steps

- x^{3} + 6 x^{2} - 7 x = 4

Move

4

to the left side

- x^{3} + 6 x^{2} - 7 x - 4 = 0

Factor

- x^{3} + 6 x^{2} - 7 x - 4 : - (x - 4) (x^{2} - 2 x - 1)

- (x - 4) (x^{2} - 2 x - 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 4 = 0 or x^{2} - 2 x - 1 = 0

Solve

x - 4 = 0 : x = 4

Solve

x^{2} - 2 x - 1 = 0 : x = 1 + 2, x = 1 - 2

The solutions are

x = 4, x = 1 + 2, x = 1 - 2

2 x^{4} - 12 x^{2} = 0

0 = 3 x^{3} + 13 x^{2} - 10 x

x^{6} - 19 x^{3} = 216

f^{3} = 343

m^{3} - m^{2} + m - 1 = 0

What are the solutions to the equation -x^3+6x^2-7x=4 ?
The solutions to the equation -x^3+6x^2-7x=4 are x=4,x=1+sqrt(2),x=1-sqrt(2)
Find the zeros of -x^3+6x^2-7x=4
The zeros of -x^3+6x^2-7x=4 are x=4,x=1+sqrt(2),x=1-sqrt(2)