Can you solve these equations?

Question

a) x*x+8x-9=0
b) x*x-10x+16=0
c) x*x-2x-3=0
d) x*x+12x+11=0

Answer 1

a). x*x + 8x - 9 = 0

Mathematics formulas: a.a = a²

x² + 8x - 9 = 0

Now solve the equation using the factor method.

Look at the product of the first and last coefficients: (1)(-9) = - 9.

We want two factors of - 9 whose sum middle coefficient of 8, and they are 9 and -1.

x² + 9x - x - 9 = 0

x(x + 9) -1(x + 9) = 0

Take out common factors.

(x - 1)(x + 9) = 0

x - 1 = 0 or x + 9 = 0

Take x - 1 = 0

Add 1 to each side.

x = 1

Take x + 9 = 0

Subtract 9 from each side.

x = -9

Therefore x = 1 or -9.

Answer 2

b) x*x - 10x + 16=0

Mathematics formulas: a.a = a²

x² - 10x + 16 = 0

Now solve the equation using the factor method.

Look at the product of the first and last coefficients: (1)(16) = 16.

We want two factors of 16 whose sum middle coefficient of - 10, and they are -8 and -2.

x² - 8x - 2x + 16 = 0

x(x - 8) - 2(x - 8) = 0

Take out common factors.

(x - 2)(x - 8) = 0

x - 2 = 0 or x - 8 = 0

Take x - 2 = 0

Add 2 to each side.

x = 2.

Take x - 8 = 0

Add 8 to each side.

x = 8

Therefore x = 2, 3

Comments

The solution of x*x - 10x + 16 = 0 is x = 2 and x = 8.

Answer 3

c) x*x - 2x - 3=0

Mathematics formulas: a.a = a²

x² - 2x - 3 = 0

Now solve the equation using the factor method.

Look at the product of the first and last coefficients: (1)(-3) = - 3.

We want two factors of - 3 whose sum middle coefficient of -2, and they are -3 and 1.

x² - 3x + x - 3 = 0

x(x - 3) +1(x - 3) = 0

Take out common factors.

(x + 1)(x - 3) = 0

x + 1 = 0 or x - 3 = 0

Take x + 1 = 0

Subtract 1 from each side.

x = - 1

Take x - 3 = 0

Add 3 to each side.

x = 3

Therefore x= 3, -1

Answer 4

d).  x*x + 12x + 11=0

Mathematics formulas: a.a = a²

x² + 12x + 11 = 0

Now solve the equation using the factor method.

Look at the product of the first and last coefficients: (1)(11) = 11.

We want two factors of 11 whose sum middle coefficient of 12, and they are 11 and 1.

x² + 11x + x + 11 = 0

x(x + 11) + 1(x + 11)

Take out common factors.

(x + 1)(x + 11) = 0

(x + 1) = 0 or (x + 11) = 0

Take x + 1 = 0

Subtract 1 from each side.

x = - 1

Take x + 11 = 0

Subtract 11 from each side.

x = -11

Therefore x = -1, -11