Question

Solve for X in the equation

Answer 1

Choice d is correct answer.

Explanation:

Given equation is:

2x² + 3x - 7 = x² + 5x + 39

Move all the terms of all equation using subtraction,we get

2x² + 3x - 7 - x² - 5x - 39 = 0

x² - 2x - 46 = 0 is quardatic equation.

ax²+bx+c = 0 is general quadratic equation.

x = ( -b±√b²-4ac) / 2a is qudratic formula.

comparing quadratic equation with general quadratic equation, we get

a = 1 , b = -2 and c = -46

putting above values in quadratic formula, we get

x = ( - (-2)±√(-2)²-4(1)(-46) ) / 2(1)

x = ( 2 ±√4+184) / 2

x = (2±√188) / 2

x = ( 2±√4×47) / 2

x = (2±2√47 ) / 2

x = 2( 1±√47) /2

x = 1±√47 is the solution of given equation.

Answer 2

Fourth option: x=1±√47

Explanation:

This is a quadratic equation, then we must equal to zero: Subtracting both sides of the equation x², 5x, and 39:

`2x^(2)+3x-7-x^(2)-5x-39=x^(2)+5x+39-x^(2)-5x-39`

Subtracting like terms:

`x^(2)-2x-46=0`

Applying the quadratic formula:

`ax^(2)+bx+c=0; a=1, b=-2, c=-46`

`x=\frac{-b+-\sqrt{b^(2)-4ac}}{2a}\\ x=\frac{-(-2)+-\sqrt{(-2)^(2)-4(1)(-46)}}{2(1)}\\ x=(2+-√(4+184))/(2)\\ x=(2+-√(188))/(2)\\ x=(2+-√(4(47)))/(2)\\ x=(2+-√(4)√(47))/(2)\\ x=(2+-2√(47))/(2)\\ x=(2)/(2)+- (2√(47))/(2)\\ x=1+-√(47)`