Solve 1/2 (4x^(2)-5x 10) 1/4 (7x^(2)-5x 12)

Question

Simplify the expression

\frac{7}{2} x^{4} - \frac{295}{4} x^{3} + 375 x^{2}

Evaluate

\frac{1}{2} (4 x^{2} - 5 x \times 10) \times \frac{1}{4} (7 x^{2} - 5 x \times 12)

Multiply the terms

\frac{1}{2} (4 x^{2} - 50 x) \times \frac{1}{4} (7 x^{2} - 5 x \times 12)

Multiply the terms

\frac{1}{2} (4 x^{2} - 50 x) \times \frac{1}{4} (7 x^{2} - 60 x)

Multiply the terms

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\frac{1}{8} (4 x^{2} - 50 x) (7 x^{2} - 60 x)

Multiply the first two terms

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(\frac{1}{2} x^{2} - \frac{25}{4} x) (7 x^{2} - 60 x)

Apply the distributive property

\frac{1}{2} x^{2} \times 7 x^{2} - \frac{1}{2} x^{2} \times 60 x - \frac{25}{4} x \times 7 x^{2} - (- \frac{25}{4} x \times 60 x)

Multiply the terms

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\frac{7}{2} x^{4} - \frac{1}{2} x^{2} \times 60 x - \frac{25}{4} x \times 7 x^{2} - (- \frac{25}{4} x \times 60 x)

Multiply the terms

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\frac{7}{2} x^{4} - 30 x^{3} - \frac{25}{4} x \times 7 x^{2} - (- \frac{25}{4} x \times 60 x)

Multiply the terms

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\frac{7}{2} x^{4} - 30 x^{3} - \frac{175}{4} x^{3} - (- \frac{25}{4} x \times 60 x)

Multiply the terms

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\frac{7}{2} x^{4} - 30 x^{3} - \frac{175}{4} x^{3} - (- 375 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

\frac{7}{2} x^{4} - 30 x^{3} - \frac{175}{4} x^{3} + 375 x^{2}

Solution

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\frac{7}{2} x^{4} - \frac{295}{4} x^{3} + 375 x^{2}

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Factor the expression

\frac{1}{4} x^{2} (2 x - 25) (7 x - 60)

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Find the roots

x_{1} = 0, x_{2} = \frac{60}{7}, x_{3} = \frac{25}{2}

Alternative Form

x_{1} = 0, x_{2} = 8. \dot{5} 7142 \dot{8}, x_{3} = 12.5

Evaluate

\frac{1}{2} (4 x^{2} - 5 x \times 10) \times \frac{1}{4} (7 x^{2} - 5 x \times 12)

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

\frac{1}{2} (4 x^{2} - 5 x \times 10) \times \frac{1}{4} (7 x^{2} - 5 x \times 12) = 0

Multiply the terms

\frac{1}{2} (4 x^{2} - 50 x) \times \frac{1}{4} (7 x^{2} - 5 x \times 12) = 0

Multiply the terms

\frac{1}{2} (4 x^{2} - 50 x) \times \frac{1}{4} (7 x^{2} - 60 x) = 0

Multiply the terms

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(\frac{1}{2} x^{2} - \frac{25}{4} x) (7 x^{2} - 60 x) = 0

Separate the equation into 2 possible cases

\frac{1}{2} x^{2} - \frac{25}{4} x = 0 7 x^{2} - 60 x = 0

Solve the equation

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x = 0 x = \frac{25}{2} 7 x^{2} - 60 x = 0

Solve the equation

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x = 0 x = \frac{25}{2} x = 0 x = \frac{60}{7}

Find the union

x = 0 x = \frac{25}{2} x = \frac{60}{7}

Solution

x_{1} = 0, x_{2} = \frac{60}{7}, x_{3} = \frac{25}{2}

Alternative Form

x_{1} = 0, x_{2} = 8. \dot{5} 7142 \dot{8}, x_{3} = 12.5

Show Solution