Enter Equation or Inequality
  

Solve the following equation

2y^2-3=53

Solve for y:

2y2-3 = 53

Add + 3 to both sides of the equation

2y2-3 + 3 = 53 + 3

2y2 = 56

Divide each side of the equation by 2

2y2
2
=
  
56
2

y2  =  56
  2

y  =  √56
  √2

Using our radical expression calculator, we can simplify this

y2 = 28

Take the square root of each side:

√y2= √28

y= = ±√28

Simplify √28

Checking square roots, we see that 52 = 25 and 62 = 36

Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

We do this by listing each product combo of 28 checking for integer square root values below:

√28 = √1√28

√28 = √2√14

√28 = √4√7

Find the highest integer square root

The highest factor that has an integer square root is 4

Therefore, we use the product combo √28 = √4√7

Evaluating square roots, we see that √4 = 2

Final Answer

y = ±2√7


You have 2 free calculationss remaining



What is the Answer?
y = ±2√7
How does the Equation and Inequalities Calculator work?
Free Equation and Inequalities Calculator - Solves an equation or inequality with 1 unknown variable and no exponents as well as certain absolute value equations and inequalities such as |x|=c and |ax| = c where a and c are constants. Solves square root, cube root, and other root equations in the form ax^2=c, ax^2 + b = c. Also solves radical equations in the form asqrt(bx) = c. Also solves open sentences and it will solve one step problems and two step equations. 2 step equations and one step equations and multi step equations
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What 3 formulas are used for the Equation and Inequalities Calculator?

One Step Equations (Division): cx = b x = b/c
One Step Equations (Addition): x + c = b x = b - c
One Step Equations (Subtraction): x - c = b x = b + c

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Equation and Inequalities Calculator?

equation
a statement declaring two mathematical expressions are equal
equation and inequalities
unknown
a number or value we do not know
variable
Alphabetic character representing a number
Example calculations for the Equation and Inequalities Calculator
  1. 2x=6
  2. 9w - 12<=20
  3. -y + 2 + 10y - 9 -6 >= -3 + 4y + 40 - 8y
  4. 2x - 9(x - 4) = 10
  5. |x|=-2
  6. |-4y|=-8
  7. x^2=25
  8. 2y^2=50
  9. 2y^2-3=53
  10. 2sqrt(4x)=20
  11. |2x+4|=30
  12. |x/2|<10
  13. |2x+6|-7=40
  14. (4x+10)^2=400

Equation and Inequalities Calculator Video


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