132x^2-1419x=33

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Solution for 132x^2-1419x=33 equation:


Simplifying
132x2 + -1419x = 33

Reorder the terms:
-1419x + 132x2 = 33

Solving
-1419x + 132x2 = 33

Solving for variable 'x'.

Reorder the terms:
-33 + -1419x + 132x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + -1419x + 132x2 = 0

Factor out the Greatest Common Factor (GCF), '33'.
33(-1 + -43x + 4x2) = 0

Ignore the factor 33.

Subproblem 1

Set the factor '(-1 + -43x + 4x2)' equal to zero and attempt to solve: Simplifying -1 + -43x + 4x2 = 0 Solving -1 + -43x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -10.75x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -10.75x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -10.75x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -10.75x + x2 = 0 + 0.25 -10.75x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -10.75x + x2 = 0.25 The x term is -10.75x. Take half its coefficient (-5.375). Square it (28.890625) and add it to both sides. Add '28.890625' to each side of the equation. -10.75x + 28.890625 + x2 = 0.25 + 28.890625 Reorder the terms: 28.890625 + -10.75x + x2 = 0.25 + 28.890625 Combine like terms: 0.25 + 28.890625 = 29.140625 28.890625 + -10.75x + x2 = 29.140625 Factor a perfect square on the left side: (x + -5.375)(x + -5.375) = 29.140625 Calculate the square root of the right side: 5.39820572 Break this problem into two subproblems by setting (x + -5.375) equal to 5.39820572 and -5.39820572.

Subproblem 1

x + -5.375 = 5.39820572 Simplifying x + -5.375 = 5.39820572 Reorder the terms: -5.375 + x = 5.39820572 Solving -5.375 + x = 5.39820572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.375' to each side of the equation. -5.375 + 5.375 + x = 5.39820572 + 5.375 Combine like terms: -5.375 + 5.375 = 0.000 0.000 + x = 5.39820572 + 5.375 x = 5.39820572 + 5.375 Combine like terms: 5.39820572 + 5.375 = 10.77320572 x = 10.77320572 Simplifying x = 10.77320572

Subproblem 2

x + -5.375 = -5.39820572 Simplifying x + -5.375 = -5.39820572 Reorder the terms: -5.375 + x = -5.39820572 Solving -5.375 + x = -5.39820572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.375' to each side of the equation. -5.375 + 5.375 + x = -5.39820572 + 5.375 Combine like terms: -5.375 + 5.375 = 0.000 0.000 + x = -5.39820572 + 5.375 x = -5.39820572 + 5.375 Combine like terms: -5.39820572 + 5.375 = -0.02320572 x = -0.02320572 Simplifying x = -0.02320572

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.77320572, -0.02320572}

Solution

x = {10.77320572, -0.02320572}

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