Find the

Find the number x, which if it increases by 2, then its square increases by 21 percent.

Correct result:

x =  20
y =  -0.9524

Solution:

$$\begin{gathered} q=21\mathrm{\%}=1+{\displaystyle \frac{21}{100}}=1.21 \\ (x+2{)}^2=x^2\ast q \\ (x+2{)}^2=x^2\cdot 1.21 \\ -0.21x^2+4x+4=0 \\ 0.21x^2-4x-4=0 \\ a=0.21;b=-4;c=-4 \\ D=b^2-4ac=4^2-4\cdot 0.21\cdot (-4)=19.36 \\ D>0 \\ {x}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{4\pm \sqrt{19.36}}{0.42}} \\ {x}_{1,2}=9.52380952\pm 10.4761904762 \\ {x}_1=20 \\ {x}_2=-0.952380952381 \\ \text{ Factored form of the equation: } \\ 0.21(x-20)(x+0.952380952381)=0 \\ x=x_1=20 \end{gathered}$$

Our quadratic equation calculator calculates it.

$y=x_2=(-0.9524)=-{\displaystyle \frac{20}{21}}=-0.9524$

Try another example

Showing 0 comments:

Related math problems and questions:

• Square
  Suppose the square's sides' length decreases by a 25% decrease in the content area of 28 cm². Determine the side length of the original square.
• Square sides
  If the square side increases by 28%, the square circumference increases by 11.2 meters. Find the length of the original square side.
• Unknown number 7
  Calculate unknown number whose 12th power when divided by the 9th power get a number 27 times greater than the unknown number. Determine the unknown number.
• Square side
  If we enlarge the square side a = 5m, its area will increase by 10,25%. How many percent will the side of the square increase? How many percent will it increase the circumference of the square?
• The ball
  The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
• Cuboid enlargement
  By how many percent increases the volume of cuboid if its every dimension increases by 30%?
• Unknown number 4
  I think number. When I divided its square root by its 1/9, I get a number 1. What number am I thinking?
• Completing square
  Solve the quadratic equation: m²=4m+20 using completing the square method
• Find the 2
  Find the term independent of x in the expansion of (4x³+1/2x)⁸
• Two pipes
  How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
• Unknown number 7
  16% of the unknown number is by 21 less than unknown number itself. Determine the natural unknown number.
• Two-digit number
  Digit sum of thinking two-digit natural number is 11. When it exchanging a sequence of digits, given a number which is 27 less than the thinking number. Find out which number I think.
• The sum
  The sum of the squares of two immediately following natural numbers is 1201. Find these numbers.
• The number 72
  The number 72 increase by 25%. By how much % will you have to reduce the number you created to get the number 72 again?
• Combinations
  If the number of elements increase by 3, it increases the number of combinations of the second class of these elements 5 times. How many are the elements?
• Trapezoid 15
  Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
• Substitution method
  Solve goniometric equation: sin⁴ θ - 1/cos² θ=cos² θ - 2