Solve ((6-x)(x^211)) - (x^2 -5x^4)(14-x)

Question

Simplify the expression

52 x^{2} - 10 x^{3} + 70 x^{4} - 5 x^{5}

Evaluate

((6 - x) (x^{2} \times 11)) - (x^{2} - 5 x^{4}) (14 - x)

Remove the parentheses

((6 - x) x^{2} \times 11) - (x^{2} - 5 x^{4}) (14 - x)

Multiply the terms

More Steps

11 x^{2} (6 - x) - (x^{2} - 5 x^{4}) (14 - x)

Rewrite the expression

11 x^{2} (6 - x) + (- x^{2} + 5 x^{4}) (14 - x)

Expand the expression

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66 x^{2} - 11 x^{3} + (- x^{2} + 5 x^{4}) (14 - x)

Expand the expression

More Steps

66 x^{2} - 11 x^{3} - 14 x^{2} + x^{3} + 70 x^{4} - 5 x^{5}

Subtract the terms

More Steps

52 x^{2} - 11 x^{3} + x^{3} + 70 x^{4} - 5 x^{5}

Solution

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52 x^{2} - 10 x^{3} + 70 x^{4} - 5 x^{5}

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(52 - 10 x + 70 x^{2} - 5 x^{3}) x^{2}

Show Solution

x_{1} = 0, x_{2} \approx 13.909969

Evaluate

((6 - x) (x^{2} \times 11)) - (x^{2} - 5 x^{4}) (14 - x)

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

((6 - x) (x^{2} \times 11)) - (x^{2} - 5 x^{4}) (14 - x) = 0

Use the commutative property to reorder the terms

((6 - x) \times 11 x^{2}) - (x^{2} - 5 x^{4}) (14 - x) = 0

Multiply the terms

11 x^{2} (6 - x) - (x^{2} - 5 x^{4}) (14 - x) = 0

Rewrite the expression

11 x^{2} (6 - x) + (- x^{2} + 5 x^{4}) (14 - x) = 0

Calculate

More Steps

52 x^{2} - 10 x^{3} + 70 x^{4} - 5 x^{5} = 0

Factor the expression

x^{2} (52 - 10 x + 70 x^{2} - 5 x^{3}) = 0

Separate the equation into 2 possible cases

x^{2} = 0 52 - 10 x + 70 x^{2} - 5 x^{3} = 0

The only way a power can be 0 is when the base equals 0

x = 0 52 - 10 x + 70 x^{2} - 5 x^{3} = 0

Solve the equation

x = 0 x \approx 13.909969

Solution

x_{1} = 0, x_{2} \approx 13.909969

Show Solution