Solve The Equation by Taking Square Roots Calculator

This calculator helps you solve quadratic equations by taking square roots. It's a fundamental method in algebra that works well for equations where the coefficient of x² is 1.

How to Use This Calculator

To solve a quadratic equation in the form x² + bx + c = 0 using the square roots method:

Enter the coefficient b (the number in front of x)
Enter the constant term c
Click "Calculate" to see the solutions

The calculator will show you the step-by-step solution using the square roots method.

The Method for Solving by Square Roots

The square roots method is used to solve quadratic equations of the form:

x² + bx + c = 0

The steps are:

Move the constant term to the other side: x² + bx = -c
Complete the square by adding (b/2)² to both sides
Factor the left side as a perfect square trinomial
Take the square root of both sides
Solve for x

The Formula

The solutions to the equation x² + bx + c = 0 are given by:

x = ±√(-c + (b/2)²) - b/2

This formula comes from completing the square and then taking the square root.

Worked Example

Let's solve x² + 6x + 5 = 0 using the square roots method.

Move the constant term: x² + 6x = -5
Complete the square: Add (6/2)² = 9 to both sides
x² + 6x + 9 = -5 + 9
(x + 3)² = 4
Take the square root of both sides:
x + 3 = ±√4
x + 3 = ±2
Solve for x:
x = -3 ± 2
Solutions: x = -1 and x = -5

Frequently Asked Questions

When should I use the square roots method?

Use this method when your quadratic equation is in the form x² + bx + c = 0. It's particularly useful when the coefficient of x² is 1 and the equation can be easily completed to a perfect square.

What if my equation doesn't have a coefficient of 1?

If your equation has a coefficient other than 1 (like ax² + bx + c = 0), you should use the quadratic formula instead. The square roots method only works for equations where a = 1.

Can I use this method for equations with decimals?

Yes, the square roots method works with decimal coefficients. Just enter the decimal values into the calculator and it will handle them correctly.

What if the equation has no real solutions?

The calculator will show you that the expression under the square root is negative, indicating no real solutions. This happens when the discriminant (b² - 4ac) is negative.

How accurate are the results?

The calculator provides solutions with up to 6 decimal places. For most practical purposes, this is sufficient accuracy. However, for precise scientific or engineering applications, you may need to use more advanced methods.