Solve (x^2 -7x) 22(x^2 -7x)-80

Question

Simplify the expression

22 x^{4} - 308 x^{3} + 1078 x^{2} - 80

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2 (11 x^{4} - 154 x^{3} + 539 x^{2} - 40)

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x_{1} = \frac{77 - 5929 + 88 110}{22}, x_{2} = \frac{77 - 5929 - 88 110}{22}, x_{3} = \frac{77 + 5929 - 88 110}{22}, x_{4} = \frac{77 + 5929 + 88 110}{22}

Alternative Form

x_{1} \approx - 0.262569, x_{2} \approx 0.283935, x_{3} \approx 6.716065, x_{4} \approx 7.262569

Evaluate

(x^{2} - 7 x) \times 22 (x^{2} - 7 x) - 80

To find the roots of the expression,set the expression equal to 0

(x^{2} - 7 x) \times 22 (x^{2} - 7 x) - 80 = 0

Multiply the terms

More Steps

22 (x^{2} - 7 x)^{2} - 80 = 0

Add or subtract both sides

22 (x^{2} - 7 x)^{2} = 0 + 80

Removing 0 doesn't change the value,so remove it from the expression

22 (x^{2} - 7 x)^{2} = 80

Divide both sides

\frac{22 ( x ^{2} - 7 x ) ^{2}}{22} = \frac{80}{22}

Divide the numbers

(x^{2} - 7 x)^{2} = \frac{80}{22}

Cancel out the common factor 2

(x^{2} - 7 x)^{2} = \frac{40}{11}

Take the root of both sides of the equation and remember to use both positive and negative roots

x^{2} - 7 x = \pm \frac{40}{11}

Simplify the expression

More Steps

x^{2} - 7 x = \pm \frac{2 110}{11}

Separate the equation into 2 possible cases

x^{2} - 7 x = \frac{2 110}{11} x^{2} - 7 x = - \frac{2 110}{11}

Calculate

More Steps

x = \frac{77 + 5929 + 88 110}{22} x = \frac{77 - 5929 + 88 110}{22} x^{2} - 7 x = - \frac{2 110}{11}

Calculate

More Steps

x = \frac{77 + 5929 + 88 110}{22} x = \frac{77 - 5929 + 88 110}{22} x = \frac{77 + 5929 - 88 110}{22} x = \frac{77 - 5929 - 88 110}{22}

Solution

x_{1} = \frac{77 - 5929 + 88 110}{22}, x_{2} = \frac{77 - 5929 - 88 110}{22}, x_{3} = \frac{77 + 5929 - 88 110}{22}, x_{4} = \frac{77 + 5929 + 88 110}{22}

Alternative Form

x_{1} \approx - 0.262569, x_{2} \approx 0.283935, x_{3} \approx 6.716065, x_{4} \approx 7.262569

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