solving quadratic equations with square roots

Note: In the previous example the solutions are integers. x + 1 = ± 49 x + 1 = ± 7 x = − 1 ± 7Īt this point, separate the “plus or minus” into two equations and solve each individually. X 2 + 2 x = 48 C o m p l e t e t h e s q u a r e. To complete the square, add 1 to both sides, complete the square, and then solve by extracting the roots. Next, find the value that completes the square using b = 2. Solve by completing the square: x 2 + 2 x − 48 = 0. This method allows us to solve equations that do not factor. for any real number k,Īpplying the square root property as a means of solving a quadratic equation is called extracting the root Applying the square root property as a means of solving a quadratic equation. In general, this describes the square root property For any real number k, if x 2 = k, then x = ± k. Here we see that x = ± 3 2 are solutions to the resulting equation. If we take the square root of both sides of this equation, we obtain the following: The equation 4 x 2 − 9 = 0 is in this form and can be solved by first isolating x 2. The goal in this section is to develop an alternative method that can be used to easily solve equations where b = 0, giving the form Here we use ± to write the two solutions in a more compact form. For example, we can solve 4 x 2 − 9 = 0 by factoring as follows:Ĥ x 2 − 9 = 0 ( 2 x + 3 ) ( 2 x − 3 ) = 0 2 x + 3 = 0 or 2 x − 3 = 0 2 x = − 3 2 x = 3 x = − 3 2 x = 3 2

If the quadratic expression factors, then we can solve the equation by factoring.

Quadratic equations can have two real solutions, one real solution, or no real solution-in which case there will be two complex solutions. A solution to such an equation is a root of the quadratic function defined by f ( x ) = a x 2 + b x + c. Where a, b, and c are real numbers and a ≠ 0. Recall that a quadratic equation is in standard form Any quadratic equation in the form a x 2 + b x + c = 0, where a, b, and c are real numbers and a ≠ 0.

Solving quadratic equations with square roots