Question

Solve the equation by factoring. $$ 4 x^{2}-4 x-15=0 $$

   Solve the equation by factoring.
$$
4 x^{2}-4 x-15=0
$$

Algebra and Trigonometry

Algebra and Trigonometry

James Stewart,… 3rd Edition

Chapter 1, Problem 10

Instant Answer

Solved by Expert Theresa Nguyen

07/22/2020

Step 1

Here, $a=4$, $b=-4$, and $c=-15$. Show more…

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Solve the equation by factoring. $$ 4 x^{2}-4 x-15=0 $$

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Key Concepts

Quadratic Equations

Quadratic equations are second-degree polynomial equations typically written in the standard form ax^2 + bx + c = 0, where a, b, and c are constants and a is not zero. They represent parabolic graphs and can have up to two real solutions.

Factoring Quadratic Expressions

Factoring is a method of rewriting a quadratic equation as a product of two linear factors. This process involves finding two numbers that multiply to give a product related to the coefficients of the quadratic and add to give the coefficient of the linear term, thereby simplifying the equation for easier solution.

Zero-Product Property

The zero-product property states that if the product of two expressions is zero, then at least one of the expressions must be zero. This property is fundamental in solving factored quadratic equations, as it allows one to set each factor equal to zero and solve for the variable.

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Transcript

00:01 We are trying to solve for the equation of 4x squared minus 4x minus 15 is equal to 0.

00:11 The first thing we want to do is to identify our a, b, b, and c.

00:17 A is 4, b is negative 4, and c is negative 15.

00:26 The next thing we want to do is to use the formula of x is equal to negative 4.

00:31 Negative b plus or minus square root of b squared minus 4ac over 2a.

00:41 We're going to plug a, b, and c into the formula to find our x's.

00:48 Negative of negative 4 plus or minus square root of negative 4 squared minus 4 times 4 times negative 15.

01:05 All of this is over 2 times 4.

01:11 Now we are going to break down our problem into two parts.

01:16 We're going to solve our first equation with the plus sign and the second equation with the minus sign.

01:25 So the first one is the plus sign.

01:28 It will look like negative of negative 4 plus square root of negative 4 squared minus 4 times 4 times negative 15.

01:43 All of this is over 2 times 4.

01:47 Now we're going to use algebra to solve the rest of the equation.

01:53 4 plus square root of 16 plus 2.

02:00 240 over 8.

02:06 Next, we have 4 plus square root of 256 over 8...

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