Solve the following equations by using the method of completing t… - Vidyadip

Question

Solve the following equations by using the method of completing the square:
$ 7 x^2+3 x-4=0 $

✓

Answer

$ 7 x^2+3 x-4=0 $
$ \Rightarrow 49 x^2+21 x-28=0(\text { Multiplying both sides by } 7)$
$ \Rightarrow 49 x^2+21 x=28$
$\Rightarrow(\text{7x})^2+2\times\text{7x}\times\frac{3}{2}+\Big(\frac{3}{2}\Big)^2\\=28+\Big(\frac{3}{2}\Big)^2$ $\Big[$Adding $\Big(\frac{3}2{}\Big)^2$ on both sides$\Big]$
$\Rightarrow\Big(\text{7x}+\frac{3}{2}\Big)^2$
$=29+\frac{9}{4}$
$=\frac{121}{4}=\Big(\frac{11}{2}\Big)^2$
$\Rightarrow\text{7x}-\frac{3}{2}=\pm\frac{11}{2}$ (Taking square root on both sides)
$\Rightarrow\text{7x}+\frac{3}{2}=\frac{11}{2}$ or $\text{7x}+\frac{3}{2}=-\frac{11}{2}$
$\Rightarrow\text{7x}=\frac{11}{2}-\frac{3}{2}=\frac{8}{2}=4$ or $\text{7x}=-\frac{11}{2}-\frac{3}{2}=-\frac{14}{2}=-7$
$\Rightarrow\text{x}=\frac{4}{7}$ or $x = -1$
Hence, $\frac{4}{7}$ and $-1$ are the roots of the given equation.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "4 Marks Questions" from Quadratic Equations→Quadratic Equations — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

Is it possible to design a rectangular park of perimeter 80m and area $400m^2.$ If so, find its length and breadth.

Solve the following system of equations graphically:
$3x + y + 1 = 0,$
$2x - 3y + 8 = 0$

Use remainder theorem to find the value of $k$, it being given that when $\mathrm{p}(\mathrm{x})=\mathrm{x}^3+2 \mathrm{x}^2+\mathrm{kx}+3$ is divided by $(x - 3),$ then the remainder is $21.$

Determine, graphically, the vertices of the triangles formed by the lines $y = x, 3y = x, x + y = 8.$

A chord of a circle of radius $14\ cm$ makes a right angle at the centre. Find the areas of the minor and major segments of the circle.

$A(6, 1), B(8, 2)$ and $C(9, 4)$ are the vertices of a parallelogram $ABCD$. If $E$ is the midpoint of $DC$, find the area of $\triangle\text{ADE}.$

Solve the following systems of equations:
$\frac{2}{3\text{x}+2\text{y}}+\frac{3}{3\text{x}-2\text{y}}=\frac{17}{5},$
$\frac{5}{3\text{x}+2\text{y}}+\frac{1}{3\text{x}-2\text{y}}=2.$

Sum of the areas of two squares is $640m^2$. If the difference of their perimeters is $64\ m$. Find the sides of the two squares.

Find the missing frequencies in the following distribution, if the sum of the frequencies is $120$ and the mean is $50.$

Class:	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
Frequency:	$17$	$f_1$	$32$	$f_2$	$19$

The sides of certain triangles are given below. Determine them are right triangles:
$7\ cm, 24\ cm, 25\ cm.$