Exercise 10 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 - 9x = - 19 ⇔ x^2 - 9x + 19 = 0 Now, we can identify the values of a, b, and c. x^2 - 9x + 19 = 0 ⇕ 1x^2+( - 9)x+ 19=0 We see that a= 1, b= - 9, and c= 19. Let's substitute these values into the Quadratic Formula.

x=- b±sqrt(b^2-4ac)/2a

SubstituteValues

Substitute values

x=- ( -9)±sqrt(( - 9)^2-4( 1)( 19))/2( 1)

▼

Solve for x and Simplify

NegNeg

- (- a)=a

x=9±sqrt((- 9)^2-4(1)(19))/2(1)

CalcPow

Calculate power

x=9±sqrt(81-4(1)(19))/2(1)

Multiply

Multiply

x=9±sqrt(81 - 76)/2

SubTerm

Subtract term

x=9±sqrt(5)/2

The solutions for this equation are x= 9± sqrt(5)2.