Solve Quadratic Equations 2x^2 + x - 5 = 0 x^2 + 8x + 7 = 0 Solve a \"quadratic-

Question

Solve Quadratic Equations 2x^2 + x - 5 = 0 x^2 + 8x + 7 = 0 Solve a "quadratic-like" equation x^2/3 - 9x^1/3 + 8 = 0 11x^2 - 18 = x^4 Solve by completing the square x^2 + 6x + 5 = 0 6x^2 - x - 2 = 0 Solve using the Quadratic Formula 4x^2 + 2x = -3 Solve Linear Equations 2/3 x - 6 = 7/5 x Solve Proportions Solve: 3x - 2/5 = 6x - 5/11 Solve Equations Involving Logarithms log (x) + log (2x) = 5 In (x) = In (2x - 3) log_2 (x) = 8 Solve Exponential Equations e^3x-4 9x = 3^x+8 3^x+1 = 7 Solve Radical Equations Solve: squareroot x - 1 = x - 7 Write a complex number in the form a + bi i^3 (5 + i) (3- squareroot -9) (3-i) (4 + 9i) 2/I 5 + I/2-i

Explanation / Answer

9. a) On using the quadratic formula, x = [ -2±{22 -4*2*(-5)}]/2*2 = (-2±44)/4 = (-1±11)/2.

b) x2 +8x +7 = 0 or, X2 +7x +x+7= 0 or, x(x+7)+1(x+7) = 0 or, (x+7)(x+1) = 0. Hence x = -7 or, x = -1.

10. a) Let x1/3 = y. Then y2 -9y +8 = 0 or, y2 -8y-y +8= 0 or, y(y-8) -1(y-8) = 0 or, (y-1)(y-8) = 0. Therefore, y = 1 0r y = 8. Hence x1/3 = 1 or x1/3 = 8. Then x = 1 or, x = 512.

b) Let x2= y. Then 11y -18 = y2or, y2-11y +18 = 0 or, y2-9y -2y +18 or, y(y-9) -2(y-9) = 0 or,

    (y-9)(y-2) = 0 . Thus y = 9 or y = 2. Then x2 = 9 or x2 = 2. Thus x = ± 3 or x = ±2.

11. a) x2+6x +5 = 0 or, x2 +2*3x + 32 -4 = 0 or, (x+3)2 -22 = 0 or, ( x+3+2)(x+3-2) = 0 or, (x+5)(x+1) = 0. Hence x = -5 or, x = -1.

b) 6x2 –x -2 = 0 or, x2 –x/6 -1/3 = 0 or, x2 -2*x/12 + (1/12)2 –1/3- (1/12)2 = 0 or, (x- 1/12)2 – 49/144 = 0 or, (x-1/12)2- (7/12)2 = 0 or, (x -1/12+7/12)(x-1/12-7/12) = 0 or, (x+1/2)(x-2/3) = 0. Thus x = -1/2 or, x = 2/3.

12. 4x2+2x = -3 or 4x2 +2x +3 = 0. On using the quadratic formula, we get x = [ -2±{ (2)2-4*4*3}]/2*4 or, x = [-2±(4-48)]/8 or, x = (-2±-44))/8 or, x = (-1± i11)/4 . Thus x = -1/4+(i11)/4 or, x = -1/4 –(i11)/4.

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