Solve by (a) Completing the square (b) Using the quadratic formula 7 x^2=x+8

Name: Problem 41, Chapter 9: Algebra Form and Function
Uploaded: 2022-04-08T17:43:53-08:00
Duration: 3 min 27 s
Channel: Alison Rodriguez
Description: Solve by (a) Completing the square (b) Using the quadratic formula 7 x^2=x+8

Solve by (a) Completing the square (b) Using the quadratic...

Key Concepts

Quadratic Equations

A quadratic equation is a second-degree polynomial equation usually written in the standard form ax² + bx + c = 0. It represents a parabola when graphed and has at most two real solutions. Understanding this form is crucial for applying various solving methods.

Standard Form

Expressing a quadratic equation in standard form, ax² + bx + c = 0, is essential as it allows for the systematic application of solution techniques like completing the square or the quadratic formula. This form clearly identifies the coefficients needed for these procedures.

Completing the Square

Completing the square is a method for solving quadratic equations by rewriting the equation as a perfect square trinomial plus a constant. This transformation simplifies the equation, making it easier to solve by isolating the variable, especially when extracting roots.

Quadratic Formula

The quadratic formula, x = (-b ± ?(b² - 4ac))/(2a), is a universal tool for solving any quadratic equation by directly substituting the coefficients from the standard form. It also provides insight into the nature of the roots through the discriminant, b² - 4ac, indicating whether the solutions are real or complex.

Transcript

00:01 For this problem here, we're going to start by completing the square.

00:03 So what i do is move the x over to the left -hand side, keeping the 8 on that side.

00:07 So now i'm ready to do the next, oh, i got to divide everything through by negative set or by 7 because we need to have the value of a there first.

00:15 So when i do that, i'm left with x squared, so now a is 1 like we need to.

00:19 Minus, we'll go ahead and write that as 1 -7x, and over here i have 8 over 7.

00:24 Now i'm ready to do my b over 2 squared.

00:26 So i'm going to do negative 7 times a half, because divided by 2 is the same thing as multiple.

00:30 By one half.

00:31 So i got negative 1 over 14, which squares out to 1 over 196.

00:37 So this becomes plus 1 over 196.

00:40 And over 1 .6.

00:43 So then from there, i'm ready to factor on the left hand side.

00:46 Again, really good with doing patterns.

00:48 So the x minus, and it's always b over 2 here.

00:51 So in this one, it was 1 over 14 squared.