20x^2-70x-4=0

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Solution for 20x^2-70x-4=0 equation:


Simplifying
20x2 + -70x + -4 = 0

Reorder the terms:
-4 + -70x + 20x2 = 0

Solving
-4 + -70x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -35x + 10x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + -35x + 10x2)' equal to zero and attempt to solve: Simplifying -2 + -35x + 10x2 = 0 Solving -2 + -35x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.2 + -3.5x + x2 = 0.0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -3.5x + 0.2 + x2 = 0.0 + 0.2 Reorder the terms: -0.2 + 0.2 + -3.5x + x2 = 0.0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -3.5x + x2 = 0.0 + 0.2 -3.5x + x2 = 0.0 + 0.2 Combine like terms: 0.0 + 0.2 = 0.2 -3.5x + x2 = 0.2 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 0.2 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 0.2 + 3.0625 Combine like terms: 0.2 + 3.0625 = 3.2625 3.0625 + -3.5x + x2 = 3.2625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 3.2625 Calculate the square root of the right side: 1.806239187 Break this problem into two subproblems by setting (x + -1.75) equal to 1.806239187 and -1.806239187.

Subproblem 1

x + -1.75 = 1.806239187 Simplifying x + -1.75 = 1.806239187 Reorder the terms: -1.75 + x = 1.806239187 Solving -1.75 + x = 1.806239187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.806239187 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.806239187 + 1.75 x = 1.806239187 + 1.75 Combine like terms: 1.806239187 + 1.75 = 3.556239187 x = 3.556239187 Simplifying x = 3.556239187

Subproblem 2

x + -1.75 = -1.806239187 Simplifying x + -1.75 = -1.806239187 Reorder the terms: -1.75 + x = -1.806239187 Solving -1.75 + x = -1.806239187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.806239187 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.806239187 + 1.75 x = -1.806239187 + 1.75 Combine like terms: -1.806239187 + 1.75 = -0.056239187 x = -0.056239187 Simplifying x = -0.056239187

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.556239187, -0.056239187}

Solution

x = {3.556239187, -0.056239187}

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