-0.57x^2+30.48x+119.85=197

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Solution for -0.57x^2+30.48x+119.85=197 equation:


Simplifying
-0.57x2 + 30.48x + 119.85 = 197

Reorder the terms:
119.85 + 30.48x + -0.57x2 = 197

Solving
119.85 + 30.48x + -0.57x2 = 197

Solving for variable 'x'.

Reorder the terms:
119.85 + -197 + 30.48x + -0.57x2 = 197 + -197

Combine like terms: 119.85 + -197 = -77.15
-77.15 + 30.48x + -0.57x2 = 197 + -197

Combine like terms: 197 + -197 = 0
-77.15 + 30.48x + -0.57x2 = 0

Begin completing the square.  Divide all terms by
-0.57 the coefficient of the squared term: 

Divide each side by '-0.57'.
135.3508772 + -53.47368421x + x2 = 0

Move the constant term to the right:

Add '-135.3508772' to each side of the equation.
135.3508772 + -53.47368421x + -135.3508772 + x2 = 0 + -135.3508772

Reorder the terms:
135.3508772 + -135.3508772 + -53.47368421x + x2 = 0 + -135.3508772

Combine like terms: 135.3508772 + -135.3508772 = 0.0000000
0.0000000 + -53.47368421x + x2 = 0 + -135.3508772
-53.47368421x + x2 = 0 + -135.3508772

Combine like terms: 0 + -135.3508772 = -135.3508772
-53.47368421x + x2 = -135.3508772

The x term is -53.47368421x.  Take half its coefficient (-26.73684211).
Square it (714.8587260) and add it to both sides.

Add '714.8587260' to each side of the equation.
-53.47368421x + 714.8587260 + x2 = -135.3508772 + 714.8587260

Reorder the terms:
714.8587260 + -53.47368421x + x2 = -135.3508772 + 714.8587260

Combine like terms: -135.3508772 + 714.8587260 = 579.5078488
714.8587260 + -53.47368421x + x2 = 579.5078488

Factor a perfect square on the left side:
(x + -26.73684211)(x + -26.73684211) = 579.5078488

Calculate the square root of the right side: 24.072969256

Break this problem into two subproblems by setting 
(x + -26.73684211) equal to 24.072969256 and -24.072969256.

Subproblem 1

x + -26.73684211 = 24.072969256 Simplifying x + -26.73684211 = 24.072969256 Reorder the terms: -26.73684211 + x = 24.072969256 Solving -26.73684211 + x = 24.072969256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.73684211' to each side of the equation. -26.73684211 + 26.73684211 + x = 24.072969256 + 26.73684211 Combine like terms: -26.73684211 + 26.73684211 = 0.00000000 0.00000000 + x = 24.072969256 + 26.73684211 x = 24.072969256 + 26.73684211 Combine like terms: 24.072969256 + 26.73684211 = 50.809811366 x = 50.809811366 Simplifying x = 50.809811366

Subproblem 2

x + -26.73684211 = -24.072969256 Simplifying x + -26.73684211 = -24.072969256 Reorder the terms: -26.73684211 + x = -24.072969256 Solving -26.73684211 + x = -24.072969256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26.73684211' to each side of the equation. -26.73684211 + 26.73684211 + x = -24.072969256 + 26.73684211 Combine like terms: -26.73684211 + 26.73684211 = 0.00000000 0.00000000 + x = -24.072969256 + 26.73684211 x = -24.072969256 + 26.73684211 Combine like terms: -24.072969256 + 26.73684211 = 2.663872854 x = 2.663872854 Simplifying x = 2.663872854

Solution

The solution to the problem is based on the solutions from the subproblems. x = {50.809811366, 2.663872854}

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