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Chapter 0: Problem 109

Solve each quadratic equation by the method of your choice. $$2 x^{2}-7 x=0$$

Short Answer

Expert verified
The solutions to the equation are \(x = 0\) and \(x = 3.5\).

Step by step solution

01

Simplify the equation

The equation is given as \(2x^2 - 7x = 0\). However, this equation can be simplified by factoring out the common factor, which in this case is \(x\). So the equation becomes \(x(2x - 7) = 0\).
02

Apply zero-product property

According to the zero-product property, if a product of factors equals zero, then at least one of the factors must be zero. So, to solve for \(x\), set each factor equal to zero and solve each equation. This gives us \(x = 0\) and \(2x - 7 = 0\).
03

Solve each equation

To solve the equation \(2x - 7 = 0\), add 7 to both sides and divide by 2. This gives us \(x = \frac{7}{2} = 3.5\).

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Most popular questions from this chapter

What is a quadratic equation?

Perform the indicated operations. Simplify the result, if possible. $$\frac{1}{x^{2}-2 x-8} \div\left(\frac{1}{x-4}-\frac{1}{x+2}\right)$$

Explain why \(|x|<-4\) has no solution.

Place the correct symbol, \(>\) or \(<\), in the shaded area between the given numbers. Do not use a calculator. Then check your result with a calculator. \(a, 3^{\frac{1}{2}}\square 3^{1}\) b. \(\sqrt{7}+\sqrt{18} \square \sqrt{7+18}\)

Perform the indicated operations. Simplify the result, if possible. $$\left(\frac{1}{a^{3}-b^{3}} \cdot \frac{a c+a d-b c-b d}{1}\right)-\frac{c-d}{a^{2}+a b+b^{2}}$$
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