What are the solutions to the equation solvefor x,x*(x+1)=h(x)^2 ?

The solutions to the equation solvefor x,x*(x+1)=h(x)^2 are x=0,x=-1/(1-h);\quad h\ne 1

Find the zeros of solvefor x,x*(x+1)=h(x)^2

The zeros of solvefor x,x*(x+1)=h(x)^2 are x=0,x=-1/(1-h);\quad h\ne 1

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solve for

x, x \cdot (x + 1) = h (x)^{2}

x = 0, x = - \frac{1}{1 - h}; h \neq = 1

Solution steps

x (x + 1) = h x^{2}

Move

h x^{2}

to the left side

x (x + 1) - h x^{2} = 0

Factor

x (x + 1) - h x^{2} : x (1 + x - x h)

x (1 + x - x h) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 1 + x - x h = 0

Solve

1 + x - x h = 0 : x = - \frac{1}{1 - h}; h \neq = 1

The solutions to the quadratic equation are:

x = 0, x = - \frac{1}{1 - h}; h \neq = 1

- x^{2} + 2 y^{2} - 20 y - 6 = 0

\frac{( x - 1 ) ^{2}}{64} - \frac{( y - 2 ) ^{2}}{32} = 1

- x^{2} + 9 y^{2} - 36 y + 27 = 0

(\frac{y - 4}{16})^{2} - (\frac{x - 6}{4})^{2} = 1

\frac{( x - 1 ) ^{2}}{49} - \frac{( y + 3 ) ^{2}}{9} = 1

What are the solutions to the equation solvefor x,x*(x+1)=h(x)^2 ?
The solutions to the equation solvefor x,x*(x+1)=h(x)^2 are x=0,x=-1/(1-h);\quad h\ne 1
Find the zeros of solvefor x,x*(x+1)=h(x)^2
The zeros of solvefor x,x*(x+1)=h(x)^2 are x=0,x=-1/(1-h);\quad h\ne 1