(x + 15)^2 - 10 = 0 Text Lesser X = Text Greater X =

2 min read Jun 08, 2024

Solving the Quadratic Equation: (x + 15)^2 - 10 = 0

In this article, we will solve the quadratic equation (x + 15)^2 - 10 = 0 and find the values of x that satisfy the equation.

First, let's expand the equation using the binomial theorem:

(x + 15)^2 = x^2 + 30x + 225

So, the equation becomes:

x^2 + 30x + 225 - 10 = 0

Simplifying the equation, we get:

x^2 + 30x + 215 = 0

Unfortunately, the equation cannot be factored easily. Therefore, we will use the quadratic formula to solve for x.

The quadratic formula is:

x = (-b ± √(b^2 - 4ac)) / 2a

In our case, a = 1, b = 30, and c = 215.

x = (-(30) ± √((30)^2 - 4(1)(215))) / 2(1)

x = (-30 ± √(900 - 860)) / 2

x = (-30 ± √40) / 2

x = (-30 ± 2√10) / 2

Now, we have two possible values for x:

x = (-30 + 2√10) / 2

x = (-30 - 2√10) / 2

We can simplify the solutions by dividing the numerator and denominator of each expression by 2:

x = -15 + √10

x = -15 - √10

Comparing the two values of x, we can conclude that:

Lesser value of x: x = -15 - √10 ≈ -22.16

Greater value of x: x = -15 + √10 ≈ -7.84

Therefore, the values of x that satisfy the equation (x + 15)^2 - 10 = 0 are x ≈ -22.16 and x ≈ -7.84.