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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?
Wiki User
∙ 6y ago
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)
Wiki User
∙ 6y ago
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What are the points of intersection of x - y equals 2 and x square - 4y square equals 5?
Rearrange the first equation to y = 2-x and then substitute this into the second equation to form the quadratic equation: -3y2+4y-1 = 0 and when solved y = 3 or y = 1/3 Points of intersection are: (3,1) and (2 and 1/3, 1/3)
11 x 2 -34 x 3 equals to 0 by Completing Square From Quadratic Equation?
If you mean: 11x2-34x+3 = 0 then the solutions are x = 1/11 and x = 3 by completing the square or using the quadratic equation formula
Solve by completing square 2x² - 6x plus 7 equals 0?
This quadratic equation has no solutions because the discriminant is less than zero.
What are the possible values of k when the line y equals 2x plus k meets the curve of y equals x square -8x -7 at two distinct real points and at one point only showing work?
The point(s) of intersection must satisfy both equations.So2x + k = x2 - 8x - 7Or, x2 - 10x - 7 - k = 0The discriminant for this quadratic equation is (-10)2 - 4*1*(-7-k)= 100 + 28 + 4k= 128 + 4kFor there to be 2 real distinct points of intersection, discriminant > 0that is 128 + 4k > 04k > -128 so that k > -32.For there to be a single point of intersection, discriminant = 0 so that k = -32.
What is the length of the straight line equation of y equals 17 minus 3x that spans the parabola of y equals x squared plus 2x minus 7 at two distinctive points?
Equations: x2+2x-7 = 17-3x Quadratic equation: x2+5x-24 = 0 Points of intersection: (-8, 41) and (3, 8) Length of line: (-8-3)2+(41-8)2 = 1210 and the square root of this is the length of the line which is about 34.78505426 or to be exact it is 11 times the square root of 10.
What are the points of intersection of x - y equals 2 and x square - 4y square equals 5?
Rearrange the first equation to y = 2-x and then substitute this into the second equation to form the quadratic equation: -3y2+4y-1 = 0 and when solved y = 3 or y = 1/3 Points of intersection are: (3,1) and (2 and 1/3, 1/3)
If you have a circle and a square what is the maximum number of points of intersection that the shapes can share?
If the circle is inside the square, four.
What is the maximum number of points of intersection between a circle and a square that lie in the same plane?
8
At what points do the equations x minus y equals 0 and x square plus y square equals 18 intersect showing detais of your homework?
x-y = 0 => x = y x2+y2 = 18 => y2+y2 = 18 2y2 =18 Divide both sides by 2 and the square root both side: y = 3 Therfore the points of intersection are: (3, 3) and (-3, -3)
11 x 2 -34 x 3 equals to 0 by Completing Square From Quadratic Equation?
If you mean: 11x2-34x+3 = 0 then the solutions are x = 1/11 and x = 3 by completing the square or using the quadratic equation formula
Solve 3x2-12x equals 15 using the method of completing the square?
Divide all terms by 3 so:- x2-4x = 5 Completing the square:- (x-2)2 = 9 x-2 = -/+3 x = -1 or x = 5
What is the fifth step in solving the equation by completing the square 5x2-12x plus 4 equals 0?
x = 2 or x = 2/5
Solve by completing square 2x² - 6x plus 7 equals 0?
This quadratic equation has no solutions because the discriminant is less than zero.
What are the possible values of k when the line y equals 2x plus k meets the curve of y equals x square -8x -7 at two distinct real points and at one point only showing work?
The point(s) of intersection must satisfy both equations.So2x + k = x2 - 8x - 7Or, x2 - 10x - 7 - k = 0The discriminant for this quadratic equation is (-10)2 - 4*1*(-7-k)= 100 + 28 + 4k= 128 + 4kFor there to be 2 real distinct points of intersection, discriminant > 0that is 128 + 4k > 04k > -128 so that k > -32.For there to be a single point of intersection, discriminant = 0 so that k = -32.
What is the length of the straight line equation of y equals 17 minus 3x that spans the parabola of y equals x squared plus 2x minus 7 at two distinctive points?
Equations: x2+2x-7 = 17-3x Quadratic equation: x2+5x-24 = 0 Points of intersection: (-8, 41) and (3, 8) Length of line: (-8-3)2+(41-8)2 = 1210 and the square root of this is the length of the line which is about 34.78505426 or to be exact it is 11 times the square root of 10.
What is an example of completing the square?
Completing the square would be the same as "Finding the square root" So an example would be 16. 16 is a perfect square so it would reduce to 4.
How do you solve 8x2 plus 14x plus 5 equals 0 by completing the square?
Please do not remove this question from Inappropriate or split any alts from it. Thanks!
