Exercise 33 Page 137

We will use the Quadratic Formula to solve the given quadratic equation. ax^2+ bx+ c=0 ⇕ x=- b± sqrt(b^2-4 a c)/2 a Let's start by rewriting the equation so all of the terms are on the left-hand side. x^2 = - 7x - 5 ⇔ x^2 + 7x + 5 = 0 Now, we can identify the values of a, b, and c. x^2 + 7x + 5 =0 ⇕ 1x^2+ 7x+ 5=0 We see that a= 1, b= 7, and c= 5. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- 7±sqrt(7^2-4( 1)( 5))/2( 1)

▼

Solve for x and Simplify

CalcPow

Calculate power

x=-7±sqrt(49-4(1)(5))/2(1)

Multiply

Multiply

x=-7±sqrt(49-20)/2

SubTerm

Subtract term

x=-7±sqrt(29)/2

The solutions for this equation are x= -7± sqrt(29)2. Let's separate them into the positive and negative cases.

x=-7± sqrt(29)/2
x_1=- 7 - sqrt(29)/2	x_2=- 7 + sqrt(29)/2
x_1≈ - 6.2	x_2 ≈ - 0.8

Using the Quadratic Formula, we found that the solutions of the given equation are x_1 ≈ - 6.2 and x_2≈ - 0.8.