x^2-5x-3=40

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Solution for x^2-5x-3=40 equation:


Simplifying
x2 + -5x + -3 = 40

Reorder the terms:
-3 + -5x + x2 = 40

Solving
-3 + -5x + x2 = 40

Solving for variable 'x'.

Reorder the terms:
-3 + -40 + -5x + x2 = 40 + -40

Combine like terms: -3 + -40 = -43
-43 + -5x + x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-43 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -5x + 43 + x2 = 0 + 43

Reorder the terms:
-43 + 43 + -5x + x2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -5x + x2 = 0 + 43
-5x + x2 = 0 + 43

Combine like terms: 0 + 43 = 43
-5x + x2 = 43

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 43 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 43 + 6.25

Combine like terms: 43 + 6.25 = 49.25
6.25 + -5x + x2 = 49.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 49.25

Calculate the square root of the right side: 7.017834424

Break this problem into two subproblems by setting 
(x + -2.5) equal to 7.017834424 and -7.017834424.

Subproblem 1

x + -2.5 = 7.017834424 Simplifying x + -2.5 = 7.017834424 Reorder the terms: -2.5 + x = 7.017834424 Solving -2.5 + x = 7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 7.017834424 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 7.017834424 + 2.5 x = 7.017834424 + 2.5 Combine like terms: 7.017834424 + 2.5 = 9.517834424 x = 9.517834424 Simplifying x = 9.517834424

Subproblem 2

x + -2.5 = -7.017834424 Simplifying x + -2.5 = -7.017834424 Reorder the terms: -2.5 + x = -7.017834424 Solving -2.5 + x = -7.017834424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -7.017834424 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -7.017834424 + 2.5 x = -7.017834424 + 2.5 Combine like terms: -7.017834424 + 2.5 = -4.517834424 x = -4.517834424 Simplifying x = -4.517834424

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.517834424, -4.517834424}

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