What are the solutions to the equation (x)=(x^2+7x-8)^2 ?

The solutions to the equation (x)=(x^2+7x-8)^2 are x\approx 0.89370…,x\approx 1.11588…

Find the zeros of (x)=(x^2+7x-8)^2

The zeros of (x)=(x^2+7x-8)^2 are x\approx 0.89370…,x\approx 1.11588…

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(x) = (x^{2} + 7 x - 8)^{2}

x \approx 0.89370 \dots, x \approx 1.11588 \dots

Solution steps

(x) = (x^{2} + 7 x - 8)^{2}

Expand

(x^{2} + 7 x - 8)^{2} : x^{4} + 14 x^{3} + 33 x^{2} - 112 x + 64

x = x^{4} + 14 x^{3} + 33 x^{2} - 112 x + 64

Switch sides

x^{4} + 14 x^{3} + 33 x^{2} - 112 x + 64 = x

Move

x

to the left side

x^{4} + 14 x^{3} + 33 x^{2} - 113 x + 64 = 0

Find one solution for

x^{4} + 14 x^{3} + 33 x^{2} - 113 x + 64 = 0

using Newton-Raphson:

x \approx 0.89370 \dots

Apply long division:

\frac{x ^{4} + 14 x ^{3} + 33 x ^{2} - 113 x + 64}{x - 0.89370 \dots} = x^{3} + 14.89370 \dots x^{2} + 46.31057 \dots x - 71.61202 \dots

x^{3} + 14.89370 \dots x^{2} + 46.31057 \dots x - 71.61202 \dots \approx 0

Find one solution for

x^{3} + 14.89370 \dots x^{2} + 46.31057 \dots x - 71.61202 \dots = 0

using Newton-Raphson:

x \approx 1.11588 \dots

Apply long division:

\frac{x ^{3} + 14.89370 \dots x ^{2} + 46.31057 \dots x - 71.61202 \dots}{x - 1.11588 \dots} = x^{2} + 16.00958 \dots x + 64.17535 \dots

x^{2} + 16.00958 \dots x + 64.17535 \dots \approx 0

Find one solution for

x^{2} + 16.00958 \dots x + 64.17535 \dots = 0

using Newton-Raphson:

No Solution for

x \in R

The solutions are

x \approx 0.89370 \dots, x \approx 1.11588 \dots

- 3 (x - 1) + 8 (x^{3}) = 6 x + 7 - 5 x

0 = 4 x^{3} - 4 x^{2} - 4

- 4 x^{3} - 4 x = 0

2 y^{3} + y^{2} - 13 y - 6 y = \frac{2}{3}

(x + 1) (- 3 x^{2} + 9 x + 30) = 0

What are the solutions to the equation (x)=(x^2+7x-8)^2 ?
The solutions to the equation (x)=(x^2+7x-8)^2 are x\approx 0.89370…,x\approx 1.11588…
Find the zeros of (x)=(x^2+7x-8)^2
The zeros of (x)=(x^2+7x-8)^2 are x\approx 0.89370…,x\approx 1.11588…