(x+11)(x-6) x^2 + 5x - 66 = 0
11 and 11. In general, you can write an equation (or two equations), and solve with the quadratic formula, to solve this type of questions.
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The tangent to 2x3 - 3x2 - 8x + 9 at x = 2 is y = 4x - 11 The tangent to y = 2x3 - 3x2 - 8x + 9 at x = 2 has the same gradient as the curve at that point; to find the gradient, differentiate: dy/dx = 6x2 - 6x - 8 which at x = 2 is: gradient = 6 x 22 - 6 x 2 - 8 = 4 At x = 2, y = 2 x 23 - 3 x 22 - 8 x 2 + 9 = -3 The equation of a line through point (xo, yo) with gradient m is: y - yo = m(x - xo) Thus the equation of the tangent to the line at x = 2 is: y - -3 = 4(x - 2) ⇒ y = 4x - 11
the solution is the answer to the equation. A solution is any value that makes the equation true. x + 2 = 10 has exactly one solution ....x=8 x + 2 > 10 has infinitely many solutions....x=9 or 10 or 11 or 12 or 13, etc
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Just write the equation as: (x - 11)(x - 3) = 0 and convert it to any form you like.
(x+11)(x-6) x^2 + 5x - 66 = 0
x2+11x+11 = 7x+9 x2+11x-7x+11-9 = 0 x2+4x+2 = 0 The above quadratic equation can be solved by using the quadratic equation formula and it will have two solutions.
There are two solutions for x: x=11 and x=-7
2x2-10+7 = 0 Solving the quadratic equation using the quadratic formula will give you two solutions and they are: x = (5 - the square root of 11)/2 or x = (5 + the square root of 11)/2
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
With difficulty because the discriminant of the quadratic equation is less than zero meaning it has no solutions
-3x2+12x-1 = y Solve the quadratic equation when y = 0 by means of the quadratic equation formula which gives x values of 3.914854216 and 0.085145784. Add these values together and divide them by 2 which is 4/2 = 2 and this is the line symmetry of the parabola. Substitute 2 for x into the original equation to find the value of y: So the vertex is at (2, 11) Remember that the parabola has a maximum value because the coefficient of x2 is negative in other words it will face downwards.
1st equation: x^2 -xy -y squared = -11 2nd equation: 2x+y = 1 Combining the the two equations together gives: -x^2 +3x +10 = 0 Solving the above quadratic equation: x = 5 or x = -2 Solutions by substitution: (5, -9) and (-2, 5)
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That doesn't factor neatly. Applying the quadratic equation, we find two real solutions: 3 plus or minus 0.5 times the square root of 14 x = 4.87082869338697 x = 1.1291713066130293