(x)(x+1)=43

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Solution for (x)(x+1)=43 equation:


Simplifying
(x)(x + 1) = 43

Reorder the terms:
x(1 + x) = 43
(1 * x + x * x) = 43
(1x + x2) = 43

Solving
1x + x2 = 43

Solving for variable 'x'.

Reorder the terms:
-43 + 1x + x2 = 43 + -43

Combine like terms: 43 + -43 = 0
-43 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + 1x + 43 + x2 = 0 + 43

Reorder the terms:
-43 + 43 + 1x + x2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + 1x + x2 = 0 + 43
1x + x2 = 0 + 43

Combine like terms: 0 + 43 = 43
1x + x2 = 43

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 43 + 0.25

Reorder the terms:
0.25 + x + x2 = 43 + 0.25

Combine like terms: 43 + 0.25 = 43.25
0.25 + x + x2 = 43.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 43.25

Calculate the square root of the right side: 6.576473219

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.576473219 and -6.576473219.

Subproblem 1

x + 0.5 = 6.576473219 Simplifying x + 0.5 = 6.576473219 Reorder the terms: 0.5 + x = 6.576473219 Solving 0.5 + x = 6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.576473219 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.576473219 + -0.5 x = 6.576473219 + -0.5 Combine like terms: 6.576473219 + -0.5 = 6.076473219 x = 6.076473219 Simplifying x = 6.076473219

Subproblem 2

x + 0.5 = -6.576473219 Simplifying x + 0.5 = -6.576473219 Reorder the terms: 0.5 + x = -6.576473219 Solving 0.5 + x = -6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.576473219 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.576473219 + -0.5 x = -6.576473219 + -0.5 Combine like terms: -6.576473219 + -0.5 = -7.076473219 x = -7.076473219 Simplifying x = -7.076473219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.076473219, -7.076473219}

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