9+-35x+4x^2=0

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Solution for 9+-35x+4x^2=0 equation:


Simplifying
9 + -35x + 4x2 = 0

Solving
9 + -35x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
2.25 + -8.75x + x2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -8.75x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -8.75x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -8.75x + x2 = 0 + -2.25
-8.75x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-8.75x + x2 = -2.25

The x term is -8.75x.  Take half its coefficient (-4.375).
Square it (19.140625) and add it to both sides.

Add '19.140625' to each side of the equation.
-8.75x + 19.140625 + x2 = -2.25 + 19.140625

Reorder the terms:
19.140625 + -8.75x + x2 = -2.25 + 19.140625

Combine like terms: -2.25 + 19.140625 = 16.890625
19.140625 + -8.75x + x2 = 16.890625

Factor a perfect square on the left side:
(x + -4.375)(x + -4.375) = 16.890625

Calculate the square root of the right side: 4.109820556

Break this problem into two subproblems by setting 
(x + -4.375) equal to 4.109820556 and -4.109820556.

Subproblem 1

x + -4.375 = 4.109820556 Simplifying x + -4.375 = 4.109820556 Reorder the terms: -4.375 + x = 4.109820556 Solving -4.375 + x = 4.109820556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = 4.109820556 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 4.109820556 + 4.375 x = 4.109820556 + 4.375 Combine like terms: 4.109820556 + 4.375 = 8.484820556 x = 8.484820556 Simplifying x = 8.484820556

Subproblem 2

x + -4.375 = -4.109820556 Simplifying x + -4.375 = -4.109820556 Reorder the terms: -4.375 + x = -4.109820556 Solving -4.375 + x = -4.109820556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = -4.109820556 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -4.109820556 + 4.375 x = -4.109820556 + 4.375 Combine like terms: -4.109820556 + 4.375 = 0.265179444 x = 0.265179444 Simplifying x = 0.265179444

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.484820556, 0.265179444}

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