90=x(x)+12+45-2x

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Solution for 90=x(x)+12+45-2x equation:


Simplifying
90 = x(x) + 12 + 45 + -2x

Multiply x * x
90 = x2 + 12 + 45 + -2x

Reorder the terms:
90 = 12 + 45 + -2x + x2

Combine like terms: 12 + 45 = 57
90 = 57 + -2x + x2

Solving
90 = 57 + -2x + x2

Solving for variable 'x'.

Combine like terms: 90 + -57 = 33
33 + 2x + -1x2 = 57 + -2x + x2 + -57 + 2x + -1x2

Reorder the terms:
33 + 2x + -1x2 = 57 + -57 + -2x + 2x + x2 + -1x2

Combine like terms: 57 + -57 = 0
33 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2
33 + 2x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
33 + 2x + -1x2 = 0 + x2 + -1x2
33 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
33 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-33 + -2x + x2 = 0

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -2x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + -2x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -2x + x2 = 0 + 33
-2x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
-2x + x2 = 33

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 33 + 1

Reorder the terms:
1 + -2x + x2 = 33 + 1

Combine like terms: 33 + 1 = 34
1 + -2x + x2 = 34

Factor a perfect square on the left side:
(x + -1)(x + -1) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + -1) equal to 5.830951895 and -5.830951895.

Subproblem 1

x + -1 = 5.830951895 Simplifying x + -1 = 5.830951895 Reorder the terms: -1 + x = 5.830951895 Solving -1 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 5.830951895 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.830951895 + 1 x = 5.830951895 + 1 Combine like terms: 5.830951895 + 1 = 6.830951895 x = 6.830951895 Simplifying x = 6.830951895

Subproblem 2

x + -1 = -5.830951895 Simplifying x + -1 = -5.830951895 Reorder the terms: -1 + x = -5.830951895 Solving -1 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -5.830951895 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.830951895 + 1 x = -5.830951895 + 1 Combine like terms: -5.830951895 + 1 = -4.830951895 x = -4.830951895 Simplifying x = -4.830951895

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.830951895, -4.830951895}

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