56x 2 357 X 126 0 Solve for X Calculator

How to Use This Calculator

To solve the equation 56x² + 2357x + 1260 = 0:

1. Enter the coefficients in the calculator form: A = 56, B = 2357, C = 1260
2. Click "Calculate" to see the solutions for x
3. Review the step-by-step solution and the parabola visualization

The calculator will display the exact solutions using the quadratic formula and show a graph of the quadratic function.

Formula Explained

The quadratic equation is in the standard form:

The solutions for x are found using the quadratic formula:

Where:

• A = 56 (coefficient of x²)
• B = 2357 (coefficient of x)
• C = 1260 (constant term)

The discriminant (B² - 4AC) determines the nature of the roots:

• If positive: two distinct real roots
• If zero: one real root (repeated)
• If negative: two complex roots

Worked Example

Let's solve 56x² + 2357x + 1260 = 0 step by step:

1. Identify coefficients: A = 56, B = 2357, C = 1260
2. Calculate discriminant: D = B² - 4AC = 2357² - 4×56×1260
3. Compute D = 5,554,409 - 284,160 = 5,269,249
4. Since D > 0, there are two real roots
5. Apply quadratic formula:
   x = [-2357 ± √5,269,249] / 112
6. Calculate √5,269,249 ≈ 2295.45
7. First root: x = (-2357 + 2295.45)/112 ≈ -5.95/112 ≈ -0.0526
8. Second root: x = (-2357 - 2295.45)/112 ≈ -4652.45/112 ≈ -41.54

The exact solutions are approximately x ≈ -0.0526 and x ≈ -41.54.

Interpreting the Results

The calculator provides two solutions for x:

• The first solution is the positive root
• The second solution is the negative root

The parabola visualization shows:

• The vertex of the parabola
• The points where the parabola crosses the x-axis (roots)
• The direction of the parabola (upwards or downwards)