Solve 1 1/2 (7x-10) 1/2 x=3x

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = 0, x_{2} = 2

Evaluate

1 \frac{1}{2} \times (7 x - 10) \times \frac{1}{2} x = 3 x

Simplify

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Evaluate

1 \frac{1}{2} \times (7 x - 10) \times \frac{1}{2} x

Covert the mixed number to an improper fraction

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Convert the expressions

1 \frac{1}{2}

Multiply the denominator of the fraction by the whole number and add the numerator of the fraction

\frac{2 + 1}{2}

Add the terms

\frac{3}{2}

\frac{3}{2} (7 x - 10) \times \frac{1}{2} x

Multiply the terms

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Evaluate

\frac{3}{2} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{3}{2 \times 2}

Multiply the numbers

\frac{3}{4}

\frac{3}{4} (7 x - 10) x

Multiply the terms

\frac{3}{4} x (7 x - 10)

\frac{3}{4} x (7 x - 10) = 3 x

Expand the expression

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Evaluate

\frac{3}{4} x (7 x - 10)

Apply the distributive property

\frac{3}{4} x \times 7 x - \frac{3}{4} x \times 10

Multiply the terms

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Evaluate

\frac{3}{4} x \times 7 x

Multiply the numbers

\frac{21}{4} x \times x

Multiply the terms

\frac{21}{4} x^{2}

\frac{21}{4} x^{2} - \frac{3}{4} x \times 10

Multiply the numbers

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Evaluate

\frac{3}{4} \times 10

Reduce the numbers

\frac{3}{2} \times 5

Multiply the numbers

\frac{3 \times 5}{2}

Multiply the numbers

\frac{15}{2}

\frac{21}{4} x^{2} - \frac{15}{2} x

\frac{21}{4} x^{2} - \frac{15}{2} x = 3 x

Move the expression to the left side

\frac{21}{4} x^{2} - \frac{21}{2} x = 0

Factor the expression

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Evaluate

\frac{21}{4} x^{2} - \frac{21}{2} x

Rewrite the expression

\frac{21}{4} x \times x - \frac{21}{4} x \times 2

Factor out \frac{21}{4} x from the expression

\frac{21}{4} x (x - 2)

\frac{21}{4} x (x - 2) = 0

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

x - 2 = 0 \frac{21}{4} x = 0

Solve the equation for x

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Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 2 \frac{21}{4} x = 0

Solve the equation for x

x = 2 x = 0

Solution

x_{1} = 0, x_{2} = 2

Show Solution

Solve the quadratic equation

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