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Popular >

(x+4)^2(x-3)^2=(x+5)^2

Solution

(x + 4)^{2} (x - 3)^{2} = (x + 5)^{2}

Solution

x \approx 4.12310 \dots, x \approx 1.82842 \dots, x \approx - 3.82842 \dots, x \approx - 4.12310 \dots

Solution steps

(x + 4)^{2} (x - 3)^{2} = (x + 5)^{2}

Expand

(x + 4)^{2} (x - 3)^{2} : x^{4} + 2 x^{3} - 23 x^{2} - 24 x + 144

Expand

(x + 5)^{2} : x^{2} + 10 x + 25

x^{4} + 2 x^{3} - 23 x^{2} - 24 x + 144 = x^{2} + 10 x + 25

Move

25

to the left side

x^{4} + 2 x^{3} - 23 x^{2} - 24 x + 119 = x^{2} + 10 x

Move

10 x

to the left side

x^{4} + 2 x^{3} - 23 x^{2} - 34 x + 119 = x^{2}

Move

x^{2}

to the left side

x^{4} + 2 x^{3} - 24 x^{2} - 34 x + 119 = 0

Find one solution for

x^{4} + 2 x^{3} - 24 x^{2} - 34 x + 119 = 0

using Newton-Raphson:

x \approx 4.12310 \dots

Apply long division:

\frac{x ^{4} + 2 x ^{3} - 24 x ^{2} - 34 x + 119}{x - 4.12310 \dots} = x^{3} + 6.12310 \dots x^{2} + 1.24621 \dots x - 28.86173 \dots

x^{3} + 6.12310 \dots x^{2} + 1.24621 \dots x - 28.86173 \dots \approx 0

Find one solution for

x^{3} + 6.12310 \dots x^{2} + 1.24621 \dots x - 28.86173 \dots = 0

using Newton-Raphson:

x \approx 1.82842 \dots

Apply long division:

\frac{x ^{3} + 6.12310 \dots x ^{2} + 1.24621 \dots x - 28.86173 \dots}{x - 1.82842 \dots} = x^{2} + 7.95153 \dots x + 15.78500 \dots

x^{2} + 7.95153 \dots x + 15.78500 \dots \approx 0

Find one solution for

x^{2} + 7.95153 \dots x + 15.78500 \dots = 0

using Newton-Raphson:

x \approx - 3.82842 \dots

Apply long division:

\frac{x ^{2} + 7.95153 \dots x + 15.78500 \dots}{x + 3.82842 \dots} = x + 4.12310 \dots

x + 4.12310 \dots \approx 0

x \approx - 4.12310 \dots

The solutions are

x \approx 4.12310 \dots, x \approx 1.82842 \dots, x \approx - 3.82842 \dots, x \approx - 4.12310 \dots

Popular Examples

x^{3} = x^{5}

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