2.87x^2-12.92x-7.18=0

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Solution for 2.87x^2-12.92x-7.18=0 equation:


Simplifying
2.87x2 + -12.92x + -7.18 = 0

Reorder the terms:
-7.18 + -12.92x + 2.87x2 = 0

Solving
-7.18 + -12.92x + 2.87x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2.87 the coefficient of the squared term: 

Divide each side by '2.87'.
-2.50174216 + -4.50174216x + x2 = 0

Move the constant term to the right:

Add '2.50174216' to each side of the equation.
-2.50174216 + -4.50174216x + 2.50174216 + x2 = 0 + 2.50174216

Reorder the terms:
-2.50174216 + 2.50174216 + -4.50174216x + x2 = 0 + 2.50174216

Combine like terms: -2.50174216 + 2.50174216 = 0.00000000
0.00000000 + -4.50174216x + x2 = 0 + 2.50174216
-4.50174216x + x2 = 0 + 2.50174216

Combine like terms: 0 + 2.50174216 = 2.50174216
-4.50174216x + x2 = 2.50174216

The x term is -4.50174216x.  Take half its coefficient (-2.25087108).
Square it (5.066420619) and add it to both sides.

Add '5.066420619' to each side of the equation.
-4.50174216x + 5.066420619 + x2 = 2.50174216 + 5.066420619

Reorder the terms:
5.066420619 + -4.50174216x + x2 = 2.50174216 + 5.066420619

Combine like terms: 2.50174216 + 5.066420619 = 7.568162779
5.066420619 + -4.50174216x + x2 = 7.568162779

Factor a perfect square on the left side:
(x + -2.25087108)(x + -2.25087108) = 7.568162779

Calculate the square root of the right side: 2.751029404

Break this problem into two subproblems by setting 
(x + -2.25087108) equal to 2.751029404 and -2.751029404.

Subproblem 1

x + -2.25087108 = 2.751029404 Simplifying x + -2.25087108 = 2.751029404 Reorder the terms: -2.25087108 + x = 2.751029404 Solving -2.25087108 + x = 2.751029404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25087108' to each side of the equation. -2.25087108 + 2.25087108 + x = 2.751029404 + 2.25087108 Combine like terms: -2.25087108 + 2.25087108 = 0.00000000 0.00000000 + x = 2.751029404 + 2.25087108 x = 2.751029404 + 2.25087108 Combine like terms: 2.751029404 + 2.25087108 = 5.001900484 x = 5.001900484 Simplifying x = 5.001900484

Subproblem 2

x + -2.25087108 = -2.751029404 Simplifying x + -2.25087108 = -2.751029404 Reorder the terms: -2.25087108 + x = -2.751029404 Solving -2.25087108 + x = -2.751029404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25087108' to each side of the equation. -2.25087108 + 2.25087108 + x = -2.751029404 + 2.25087108 Combine like terms: -2.25087108 + 2.25087108 = 0.00000000 0.00000000 + x = -2.751029404 + 2.25087108 x = -2.751029404 + 2.25087108 Combine like terms: -2.751029404 + 2.25087108 = -0.500158324 x = -0.500158324 Simplifying x = -0.500158324

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.001900484, -0.500158324}

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