Question

Factorise and solve x2 + 4x - 21 = 0

Answer 1

`x=3,\:x=-7`

Key:

• When doing a quadratic equation, one thing you must always know going into the equation is that you will have more than one answer.

Explanation:

`x^2+4x-21=0\\For\:\rightarrow\quad a=1,\:b=4,\:c=-21\\x_(1,\:2)=(-4\pm √(4^2-4\cdot \:1\cdot \left(-21\right)))/(2\cdot \:1)\\√(4^2-4\cdot \:1\cdot \left(-21\right))\\=√(4^2+4\cdot \:1\cdot \:21)\\=√(4^2+84)\\=√(16+84)\\=√(100)\\=√(10^2)\\=10\\x_(1,\:2)=(-4\pm \:10)/(2\cdot \:1)\\x_1=(-4+10)/(2\cdot \:1),\:x_2=(-4-10)/(2\cdot \:1)`

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Optional: Solve for x₁ and x₂

(x₁)

`(-4+10)/(2\cdot \:1)\\=(6)/(2\cdot \:1)\\=(6)/(2)\\=3`

(x₂)

`(-4-10)/(2\cdot \:1)\\=(-14)/(2\cdot \:1)\\=(-14)/(2)\\=-(14)/(2)\\=-7`

Answer 2

x = 3 and x = -7

Explanation:

Solving :

⇒ x² + 4x - 21 = 0

⇒ x² + 7x - 3x - 21 = 0

⇒ x(x + 7) - 3(x + 7) = 0

⇒ (x - 3)(x + 7) = 0

⇒ x = 3 and x = -7