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Solve Quadratic Equations by Completing the Square: example 10.27 · Physics Playground

Exercises Roots and quadratic equations

Example 10.27 from Elementary Algebra, 10.2 Solve Quadratic Equations by Completing the Square

Solve Quadratic Equations by Completing the Square: example 10.27

Solve $3 x^{2} + 2 x = 4$ by completing the square.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

Again, our first step will be to make the coefficient of $x^{2}$ be one. By dividing both sides of the equation by the coefficient of $x^{2}$ , we can then continue with solving the equation by completing the square.


Divide both sides by 3 to make the coefficient of $x^{2}$ equal 1.
Simplify.
Take half of $\frac{2}{3}$ and square it. $(\frac{1}{2} \cdot \frac{2}{3})^{2} = \frac{1}{9}$
Add $\frac{1}{9}$ to both sides.
Factor the perfect square trinomial as a binomial square.
Use the Square Root Property.
Simplify the radical.
Solve for x.
Rewrite to show 2 solutions.
Check. We leave the check for you.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve $4 x^{2} + 3 x = 12$ by completing the square.

How did it go?

PreviousSolve Quadratic Equations by Completing the Square: example 10.26 Next Solve Quadratic Equations Using the Quadratic Formula: example 10.28

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 10.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.