50x^2+76x-6=0

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Solution for 50x^2+76x-6=0 equation:


Simplifying
50x2 + 76x + -6 = 0

Reorder the terms:
-6 + 76x + 50x2 = 0

Solving
-6 + 76x + 50x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 38x + 25x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + 38x + 25x2)' equal to zero and attempt to solve: Simplifying -3 + 38x + 25x2 = 0 Solving -3 + 38x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.12 + 1.52x + x2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + 1.52x + 0.12 + x2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + 1.52x + x2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + 1.52x + x2 = 0 + 0.12 1.52x + x2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 1.52x + x2 = 0.12 The x term is 1.52x. Take half its coefficient (0.76). Square it (0.5776) and add it to both sides. Add '0.5776' to each side of the equation. 1.52x + 0.5776 + x2 = 0.12 + 0.5776 Reorder the terms: 0.5776 + 1.52x + x2 = 0.12 + 0.5776 Combine like terms: 0.12 + 0.5776 = 0.6976 0.5776 + 1.52x + x2 = 0.6976 Factor a perfect square on the left side: (x + 0.76)(x + 0.76) = 0.6976 Calculate the square root of the right side: 0.835224521 Break this problem into two subproblems by setting (x + 0.76) equal to 0.835224521 and -0.835224521.

Subproblem 1

x + 0.76 = 0.835224521 Simplifying x + 0.76 = 0.835224521 Reorder the terms: 0.76 + x = 0.835224521 Solving 0.76 + x = 0.835224521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.76' to each side of the equation. 0.76 + -0.76 + x = 0.835224521 + -0.76 Combine like terms: 0.76 + -0.76 = 0.00 0.00 + x = 0.835224521 + -0.76 x = 0.835224521 + -0.76 Combine like terms: 0.835224521 + -0.76 = 0.075224521 x = 0.075224521 Simplifying x = 0.075224521

Subproblem 2

x + 0.76 = -0.835224521 Simplifying x + 0.76 = -0.835224521 Reorder the terms: 0.76 + x = -0.835224521 Solving 0.76 + x = -0.835224521 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.76' to each side of the equation. 0.76 + -0.76 + x = -0.835224521 + -0.76 Combine like terms: 0.76 + -0.76 = 0.00 0.00 + x = -0.835224521 + -0.76 x = -0.835224521 + -0.76 Combine like terms: -0.835224521 + -0.76 = -1.595224521 x = -1.595224521 Simplifying x = -1.595224521

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.075224521, -1.595224521}

Solution

x = {0.075224521, -1.595224521}

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