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10 votes
10 votes
X
x^(2)+ 10x =11

User Rox
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1 Answer

19 votes
19 votes

Answer:

For this problem, x has multiple values, so we will solve for both.

Explanation:


x^2+10x-11=11-11\\x^2+10x-11=0\\

Quadratic rule


x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)


\mathrm{For\:} a=1,\:b=10,\:c=-11


x_(1,\:2)=(-10\pm √(10^2-4\cdot \:1\cdot \left(-11\right)))/(2\cdot \:1)

Dealing with radicals


√(10^2-4\cdot \:1\cdot \left(-11\right))\\=√(10^2+4\cdot \:1\cdot \:11)\\=√(10^2+44)\\=√(100+44)\\=√(144)\\=√(12^2)\\=12\\

Multi-solution expression


x_1=(-10+12)/(2\cdot \:1),\:x_2=(-10-12)/(2\cdot \:1)

Solve for x₁


(-10+12)/(2\cdot \:1)\\=(2)/(2\cdot \:1)\\=(2)/(2)\\=1

Solve for x₂


(-10-12)/(2\cdot \:1)\\=(-22)/(2\cdot \:1)\\=(-22)/(2)\\= -(22)/(2)\\= -11

Thus, x has 2 values for 2 different numbers:

x₁ = 1

x₂ = -11

➲ Hope this helps!

User Jophab
by
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