Solve the following equation by the quadratic formula: \({x^2} +9x +19 =0\)
Answer
\(x = - 5.6\) or \(x = - 3.4\)
Worked Solution
Question 2
18908
Solve the following equation by the quadratic formula: \(7{x^2}+16x+9=0\)
Answer
\(x = - 1.3\,\) or \(x = - 1.0\)
Worked Solution
Question 3
18909
Solve the following equation by the quadratic formula: \(5{z^2}+18z+13=0\)
Answer
\(x = - 2.6\) or \(x = - 1\)
Worked Solution
Question 4
18910
Solve by factoring: \(x=\dfrac{{5x-6}}{x}\)
Answer
\(x = 3\) or \(x = 2\)
Worked Solution
Question 5
18911
Solve by factorising: \(x+\dfrac{3}{x}=-4\)
Answer
\(x = - 3\) or \(x = - 1\)
Worked Solution
Question 6
18912
Solve by factorising: \(\dfrac{{x+3}}{{2x-7}}=\dfrac{{2x-1}}{{x-3}}\)
Answer
\(x = \dfrac{4}{3}\) or \(x = 4\)
Worked Solution
Question 7
18913
Amy's mother is 2 years less than 5 times Amy's age. 12 years from now, the product of their ages will be 1230. What is Amy's present age?
Answer
Amy's present age is 10 years old
Worked Solution
Question 8
18914
As shown in figure, ABC is a right angles triangle with dimensions marked in cm. If its area is \(60~\text{cm}^2\), find the length of its hypotenuse AC.
Answer
Hypotenuse is 17 cm
Worked Solution
Question 9
18915
ABCD is a kite such that its longer diagonal is 10 cm longer than twice the length of diagonal BD. If its area is \(300~\text{cm}^2\). find the length of longer diagonal.
Answer
Length of diagonal is 40 cm.
Worked Solution
Question 10
25848
Solve \(x - 2 = \dfrac{8}{x}\)
Answer
\(x=-2\), \(x=4\)
Worked Solution
Question 11
13191
The solutions to \(2x^2 + x - 3=0\) are?
Answer
\(x = - 1\dfrac{1}{2},\,x = 1\)
Worked Solution
Question 12
13192
The solutions to \(x + \dfrac{2}{x}\) = \(\dfrac{9}{2}\) are?
Answer
\(x = 4,\,x = \dfrac{1}{2}\)
Worked Solution
Question 13
13193
The solutions to \({(x - 7)^2} = 64\) are?
Answer
\(x = 15\,,\,x = - 1\)
Worked Solution
Question 14
13194
The solutions to \(x = {\rm{1 + }}\dfrac{1}{x}\) are?
Answer
\(x = \dfrac{{1 \pm \sqrt 5 }}{2}\)
Worked Solution
Question 15
13195
A rectangular garden, 7m by 3m is surrounded by a concrete path of unitform width. If the area of the path is \({\rm{39}}{{\rm{m}}^3}\), then the width is?
