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What are the solutions to x2 plus xy plus y2 equals 7 and 2x plus y equals 1 shown by completing the square?
Wiki User
∙ 6y ago
If: x^2 +xy +y^2 = 7 and 2x +y =1 or y = 1 -2x
Then: x^2 +x(1-2x) +(1-2x)^2 -7 = 0
Removing brackets: x^2 +x -2x^2 +1 -4x +4x^2 -7 = 0
Collecting like terms: 3x^2 -3x -6 = 0
Dividing all terms by 3: x^2 -x -2 = 0
Completing the square: (x -1/2)^2 -1/4 -2 = 0 => (x-1/2)^2 = 2.25
Square root both sides: x -1/2 = +/- 1.5
Add 0.5 to both sides: x = 2 or x = -1
Therefore by substitution solutions are: (2, -3) and (-1, 3)
Wiki User
∙ 6y ago
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What are the solutions to 3x squared equals 6x plus 4 shown by means of completing the square?
If: 3x^2 = 6x+4 Then: 3^2 -6x-4 = 0 Divide all terms by 3: x^2 -2x-4/3 = 0 Completing the square: (x-1)^2 -7/3 = 0 => (x-1)^2 = 7/3 or as 21/9 If: (x-1)^2 = 21/9 Then: x = 1 +/- (square root 21) over 3 which are the exact solutions
How many real solutions are there to the equation shown below 4x2 plus x - 1 equals 0?
2.
What are the solutions to the simultaneous equations of 3x -5y equals 16 and xy equals 7 shown by completing the square?
If: 3x -5y = 16 then y = 0.6x -3.2 If: xy = 7 then x(0.6x -3.2) -7 = 0 Removing brackets: 0.6x^2 -3.2x -7 = 0 Dividing all terms by 0.6: x^2 -16/3x -35/3 = 0 Completing the square: (x -8/3)^2 -64/9 -35/3 = 0 => (x -8/3)^2 = 169/9 Square root both sides: x -8/3 = -13/3 or +13/3 Add 8/3 to both sides: x = -5/3 or x = 7 Solutions by substitution are: x = -5/3, y = -21/5 and x = 7, y = 1
How will you show that 5 raise to 14 equals double square root of 5?
5^14 is not equivalent to 5^(1/4), so it cannot be shown
What are the points of intersection of the line y equals x plus 1 with the curve x2 plus y2 equals 25 shown by completing the square?
If: y = x+1 then y^2 = (x+1)^2 If: x^2 +y^2 = 25 then x^2 +(x+1)^2 -25 = 0 Multiplying out the brackets: x^2 +x^2 +2x +1 -25 = 0 Collecting like terms: 2x^2 +2x -24 = 0 Dividing all terms by 2: x^2 +x -12 = 0 Completing the square: (x+0.5)^2 = 12.25 Square root both sides: x+0.5 = -3.5 or +3.5 Deducting 0.5 from both sides: x = -4 or 3 Intersections by substitution into original equations are at: (-4,-3) and (3, 4)
What are the solutions to 3x squared equals 6x plus 4 shown by means of completing the square?
If: 3x^2 = 6x+4 Then: 3^2 -6x-4 = 0 Divide all terms by 3: x^2 -2x-4/3 = 0 Completing the square: (x-1)^2 -7/3 = 0 => (x-1)^2 = 7/3 or as 21/9 If: (x-1)^2 = 21/9 Then: x = 1 +/- (square root 21) over 3 which are the exact solutions
How many real solutions are there to the equation shown below 4x2 plus x - 1 equals 0?
2.
What are the solutions to the simultaneous equations of 3x -5y equals 16 and xy equals 7 shown by completing the square?
If: 3x -5y = 16 then y = 0.6x -3.2 If: xy = 7 then x(0.6x -3.2) -7 = 0 Removing brackets: 0.6x^2 -3.2x -7 = 0 Dividing all terms by 0.6: x^2 -16/3x -35/3 = 0 Completing the square: (x -8/3)^2 -64/9 -35/3 = 0 => (x -8/3)^2 = 169/9 Square root both sides: x -8/3 = -13/3 or +13/3 Add 8/3 to both sides: x = -5/3 or x = 7 Solutions by substitution are: x = -5/3, y = -21/5 and x = 7, y = 1
How many solutions does the system of linear equations shown have?
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What are the solutions to the equation of 2x squared -x -1 equals 0 done by completing the square with work shown from start to finish?
2*x^2 - x - 1 = 02*x^2 - x = 1[x^2 - x/2] = 1/2[x^2 - x/2 + (1/4)^2] = 1/2 + (1/4)^2(x - 1/4)^2 = 1/2 + 1/16 = 9/16x - 1/4 = +/- sqrt(9/16) = +/- 3/4x = 1/4 +/- 3/4x = -1/2 or x = 1.
How will you show that 5 raise to 14 equals double square root of 5?
5^14 is not equivalent to 5^(1/4), so it cannot be shown
What are the points of intersection of the line y equals x plus 1 with the curve x2 plus y2 equals 25 shown by completing the square?
If: y = x+1 then y^2 = (x+1)^2 If: x^2 +y^2 = 25 then x^2 +(x+1)^2 -25 = 0 Multiplying out the brackets: x^2 +x^2 +2x +1 -25 = 0 Collecting like terms: 2x^2 +2x -24 = 0 Dividing all terms by 2: x^2 +x -12 = 0 Completing the square: (x+0.5)^2 = 12.25 Square root both sides: x+0.5 = -3.5 or +3.5 Deducting 0.5 from both sides: x = -4 or 3 Intersections by substitution into original equations are at: (-4,-3) and (3, 4)
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Which points are solutions to the system of inequalities shown below y 2x y 8 x 2?
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "equals", etc. There are no inequalities shown in the question.
Why is the 2 shown in the answer when measuring square area?
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There is no particular property illustrated by the equation shown.
