Solve (7x-85x^2) (4x-1)

Question

Simplify the expression

113 x^{2} - 7 x - 340 x^{3}

Evaluate

(7 x - 85 x^{2}) (4 x - 1)

Apply the distributive property

7 x \times 4 x - 7 x \times 1 - 85 x^{2} \times 4 x - (- 85 x^{2} \times 1)

Multiply the terms

More Steps

Evaluate

7 x \times 4 x

Multiply the numbers

28 x \times x

Multiply the terms

28 x^{2}

28 x^{2} - 7 x \times 1 - 85 x^{2} \times 4 x - (- 85 x^{2} \times 1)

Any expression multiplied by 1 remains the same

28 x^{2} - 7 x - 85 x^{2} \times 4 x - (- 85 x^{2} \times 1)

Multiply the terms

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Evaluate

- 85 x^{2} \times 4 x

Multiply the numbers

- 340 x^{2} \times x

Multiply the terms

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Evaluate

x^{2} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 1}

Add the numbers

x^{3}

- 340 x^{3}

28 x^{2} - 7 x - 340 x^{3} - (- 85 x^{2} \times 1)

Any expression multiplied by 1 remains the same

28 x^{2} - 7 x - 340 x^{3} - (- 85 x^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

28 x^{2} - 7 x - 340 x^{3} + 85 x^{2}

Solution

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Evaluate

28 x^{2} + 85 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(28 + 85) x^{2}

Add the numbers

113 x^{2}

113 x^{2} - 7 x - 340 x^{3}

Show Solution

Factor the expression

x (7 - 85 x) (4 x - 1)

Evaluate

(7 x - 85 x^{2}) (4 x - 1)

Solution

More Steps

Evaluate

7 x - 85 x^{2}

Rewrite the expression

x \times 7 - x \times 85 x

Factor out x from the expression

x (7 - 85 x)

x (7 - 85 x) (4 x - 1)

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{7}{85}, x_{3} = \frac{1}{4}

Alternative Form

x_{1} = 0, x_{2} \approx 0.082353, x_{3} = 0.25

Evaluate

(7 x - 85 x^{2}) (4 x - 1)

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

(7 x - 85 x^{2}) (4 x - 1) = 0

Separate the equation into 2 possible cases

7 x - 85 x^{2} = 0 4 x - 1 = 0

Solve the equation

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Evaluate

7 x - 85 x^{2} = 0

Factor the expression

More Steps

Evaluate

7 x - 85 x^{2}

Rewrite the expression

x \times 7 - x \times 85 x

Factor out x from the expression

x (7 - 85 x)

x (7 - 85 x) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 7 - 85 x = 0

Solve the equation for x

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Evaluate

7 - 85 x = 0

Move the constant to the right-hand side and change its sign

- 85 x = 0 - 7

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

- 85 x = - 7

Change the signs on both sides of the equation

85 x = 7

Divide both sides

\frac{85 x}{85} = \frac{7}{85}

Divide the numbers

x = \frac{7}{85}

x = 0 x = \frac{7}{85}

x = 0 x = \frac{7}{85} 4 x - 1 = 0

Solve the equation

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Evaluate

4 x - 1 = 0

Move the constant to the right-hand side and change its sign

4 x = 0 + 1

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

4 x = 1

Divide both sides

\frac{4 x}{4} = \frac{1}{4}

Divide the numbers

x = \frac{1}{4}

x = 0 x = \frac{7}{85} x = \frac{1}{4}

Solution

x_{1} = 0, x_{2} = \frac{7}{85}, x_{3} = \frac{1}{4}

Alternative Form

x_{1} = 0, x_{2} \approx 0.082353, x_{3} = 0.25

Show Solution