x^2+5x-33=7x-3

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Solution for x^2+5x-33=7x-3 equation:


Simplifying
x2 + 5x + -33 = 7x + -3

Reorder the terms:
-33 + 5x + x2 = 7x + -3

Reorder the terms:
-33 + 5x + x2 = -3 + 7x

Solving
-33 + 5x + x2 = -3 + 7x

Solving for variable 'x'.

Reorder the terms:
-33 + 3 + 5x + -7x + x2 = -3 + 7x + 3 + -7x

Combine like terms: -33 + 3 = -30
-30 + 5x + -7x + x2 = -3 + 7x + 3 + -7x

Combine like terms: 5x + -7x = -2x
-30 + -2x + x2 = -3 + 7x + 3 + -7x

Reorder the terms:
-30 + -2x + x2 = -3 + 3 + 7x + -7x

Combine like terms: -3 + 3 = 0
-30 + -2x + x2 = 0 + 7x + -7x
-30 + -2x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-30 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -2x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + -2x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -2x + x2 = 0 + 30
-2x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
-2x + x2 = 30

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 = 30 + 1

Reorder the terms:
1 + -2x + x2 = 30 + 1

Combine like terms: 30 + 1 = 31
1 + -2x + x2 = 31

Factor a perfect square on the left side:
(x + -1)(x + -1) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + -1) equal to 5.567764363 and -5.567764363.

Subproblem 1

x + -1 = 5.567764363 Simplifying x + -1 = 5.567764363 Reorder the terms: -1 + x = 5.567764363 Solving -1 + x = 5.567764363 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 = 5.567764363 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.567764363 + 1 x = 5.567764363 + 1 Combine like terms: 5.567764363 + 1 = 6.567764363 x = 6.567764363 Simplifying x = 6.567764363

Subproblem 2

x + -1 = -5.567764363 Simplifying x + -1 = -5.567764363 Reorder the terms: -1 + x = -5.567764363 Solving -1 + x = -5.567764363 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 = -5.567764363 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.567764363 + 1 x = -5.567764363 + 1 Combine like terms: -5.567764363 + 1 = -4.567764363 x = -4.567764363 Simplifying x = -4.567764363

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.567764363, -4.567764363}

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