x(x+0.89)=92.99

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Solution for x(x+0.89)=92.99 equation:


Simplifying
x(x + 0.89) = 92.99

Reorder the terms:
x(0.89 + x) = 92.99
(0.89 * x + x * x) = 92.99
(0.89x + x2) = 92.99

Solving
0.89x + x2 = 92.99

Solving for variable 'x'.

Reorder the terms:
-92.99 + 0.89x + x2 = 92.99 + -92.99

Combine like terms: 92.99 + -92.99 = 0.00
-92.99 + 0.89x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '92.99' to each side of the equation.
-92.99 + 0.89x + 92.99 + x2 = 0.00 + 92.99

Reorder the terms:
-92.99 + 92.99 + 0.89x + x2 = 0.00 + 92.99

Combine like terms: -92.99 + 92.99 = 0.00
0.00 + 0.89x + x2 = 0.00 + 92.99
0.89x + x2 = 0.00 + 92.99

Combine like terms: 0.00 + 92.99 = 92.99
0.89x + x2 = 92.99

The x term is 0.89x.  Take half its coefficient (0.445).
Square it (0.198025) and add it to both sides.

Add '0.198025' to each side of the equation.
0.89x + 0.198025 + x2 = 92.99 + 0.198025

Reorder the terms:
0.198025 + 0.89x + x2 = 92.99 + 0.198025

Combine like terms: 92.99 + 0.198025 = 93.188025
0.198025 + 0.89x + x2 = 93.188025

Factor a perfect square on the left side:
(x + 0.445)(x + 0.445) = 93.188025

Calculate the square root of the right side: 9.653394481

Break this problem into two subproblems by setting 
(x + 0.445) equal to 9.653394481 and -9.653394481.

Subproblem 1

x + 0.445 = 9.653394481 Simplifying x + 0.445 = 9.653394481 Reorder the terms: 0.445 + x = 9.653394481 Solving 0.445 + x = 9.653394481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.445' to each side of the equation. 0.445 + -0.445 + x = 9.653394481 + -0.445 Combine like terms: 0.445 + -0.445 = 0.000 0.000 + x = 9.653394481 + -0.445 x = 9.653394481 + -0.445 Combine like terms: 9.653394481 + -0.445 = 9.208394481 x = 9.208394481 Simplifying x = 9.208394481

Subproblem 2

x + 0.445 = -9.653394481 Simplifying x + 0.445 = -9.653394481 Reorder the terms: 0.445 + x = -9.653394481 Solving 0.445 + x = -9.653394481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.445' to each side of the equation. 0.445 + -0.445 + x = -9.653394481 + -0.445 Combine like terms: 0.445 + -0.445 = 0.000 0.000 + x = -9.653394481 + -0.445 x = -9.653394481 + -0.445 Combine like terms: -9.653394481 + -0.445 = -10.098394481 x = -10.098394481 Simplifying x = -10.098394481

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.208394481, -10.098394481}

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