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PRE-ALGEBRA EXAMPLES

Popular Problems
Pre-Algebra
Solve for x y=x^2+2x-3

y=x2+2x−3y=x2+2x-3
Step 1
Rewrite the equation as x2+2x−3=yx2+2x-3=y.
x2+2x−3=yx2+2x-3=y

Step 2
Subtract yy from both sides of the equation.
x2+2x−3−y=0x2+2x-3-y=0

Step 3
Use the quadratic formula to find the solutions.
−b±√b2−4(ac)2a-b±b2-4(ac)2a

Step 4
Substitute the values a=1a=1, b=2b=2, and c=−3−yc=-3-y into the quadratic
formula and solve for xx.
−2±√22−4⋅(1⋅(−3−y))2⋅1-2±22-4⋅(1⋅(-3-y))2⋅1

Step 5
Simplify.

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Step 5.1
Simplify the numerator.

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Step 5.1.1
Raise 22 to the power of 22.
x=−2±√4−4⋅1⋅(−3−y)2⋅1x=-2±4-4⋅1⋅(-3-y)2⋅1
Step 5.1.2
Multiply −4-4 by 11.
x=−2±√4−4⋅(−3−y)2⋅1x=-2±4-4⋅(-3-y)2⋅1
Step 5.1.3
Apply the distributive property.
x=−2±√4−4⋅−3−4(−y)2⋅1x=-2±4-4⋅-3-4(-y)2⋅1
Step 5.1.4
Multiply −4-4 by −3-3.
x=−2±√4+12−4(−y)2⋅1x=-2±4+12-4(-y)2⋅1
Step 5.1.5
Multiply −1-1 by −4-4.
x=−2±√4+12+4y2⋅1x=-2±4+12+4y2⋅1
Step 5.1.6
Add 44 and 1212.
x=−2±√16+4y2⋅1x=-2±16+4y2⋅1
Step 5.1.7
Factor 44 out of 16+4y16+4y.

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Step 5.1.7.1
Factor 44 out of 1616.
x=−2±√4⋅4+4y2⋅1x=-2±4⋅4+4y2⋅1
Step 5.1.7.2
Factor 44 out of 4⋅4+4y4⋅4+4y.
x=−2±√4(4+y)2⋅1x=-2±4(4+y)2⋅1
x=−2±√4(4+y)2⋅1x=-2±4(4+y)2⋅1
Step 5.1.8
Rewrite 4(4+y)4(4+y) as 22(22+y)22(22+y).

Tap for more steps...
Step 5.1.8.1
Rewrite 44 as 2222.
x=−2±√22(4+y)2⋅1x=-2±22(4+y)2⋅1
Step 5.1.8.2
Rewrite 44 as 2222.
x=−2±√22(22+y)2⋅1x=-2±22(22+y)2⋅1
x=−2±√22(22+y)2⋅1x=-2±22(22+y)2⋅1
Step 5.1.9
Pull terms out from under the radical.
x=−2±2√22+y2⋅1x=-2±222+y2⋅1
Step 5.1.10
Raise 22 to the power of 22.
x=−2±2√4+y2⋅1x=-2±24+y2⋅1
x=−2±2√4+y2⋅1x=-2±24+y2⋅1
Step 5.2
Multiply 22 by 11.
x=−2±2√4+y2x=-2±24+y2
Step 5.3
Simplify −2±2√4+y2-2±24+y2.
x=−1±√4+yx=-1±4+y
x=−1±√4+yx=-1±4+y

Step 6
The final answer is the combination of both solutions.
x=−1+√4+yx=-1+4+y
x=−1−√4+yx=-1-4+y

y=x2+2x−3y=x2+2x-3


yy
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