10x^2+89x-9=4

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Solution for 10x^2+89x-9=4 equation:


Simplifying
10x2 + 89x + -9 = 4

Reorder the terms:
-9 + 89x + 10x2 = 4

Solving
-9 + 89x + 10x2 = 4

Solving for variable 'x'.

Reorder the terms:
-9 + -4 + 89x + 10x2 = 4 + -4

Combine like terms: -9 + -4 = -13
-13 + 89x + 10x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-13 + 89x + 10x2 = 0

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

Divide each side by '10'.
-1.3 + 8.9x + x2 = 0

Move the constant term to the right:

Add '1.3' to each side of the equation.
-1.3 + 8.9x + 1.3 + x2 = 0 + 1.3

Reorder the terms:
-1.3 + 1.3 + 8.9x + x2 = 0 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + 8.9x + x2 = 0 + 1.3
8.9x + x2 = 0 + 1.3

Combine like terms: 0 + 1.3 = 1.3
8.9x + x2 = 1.3

The x term is 8.9x.  Take half its coefficient (4.45).
Square it (19.8025) and add it to both sides.

Add '19.8025' to each side of the equation.
8.9x + 19.8025 + x2 = 1.3 + 19.8025

Reorder the terms:
19.8025 + 8.9x + x2 = 1.3 + 19.8025

Combine like terms: 1.3 + 19.8025 = 21.1025
19.8025 + 8.9x + x2 = 21.1025

Factor a perfect square on the left side:
(x + 4.45)(x + 4.45) = 21.1025

Calculate the square root of the right side: 4.593745748

Break this problem into two subproblems by setting 
(x + 4.45) equal to 4.593745748 and -4.593745748.

Subproblem 1

x + 4.45 = 4.593745748 Simplifying x + 4.45 = 4.593745748 Reorder the terms: 4.45 + x = 4.593745748 Solving 4.45 + x = 4.593745748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.45' to each side of the equation. 4.45 + -4.45 + x = 4.593745748 + -4.45 Combine like terms: 4.45 + -4.45 = 0.00 0.00 + x = 4.593745748 + -4.45 x = 4.593745748 + -4.45 Combine like terms: 4.593745748 + -4.45 = 0.143745748 x = 0.143745748 Simplifying x = 0.143745748

Subproblem 2

x + 4.45 = -4.593745748 Simplifying x + 4.45 = -4.593745748 Reorder the terms: 4.45 + x = -4.593745748 Solving 4.45 + x = -4.593745748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.45' to each side of the equation. 4.45 + -4.45 + x = -4.593745748 + -4.45 Combine like terms: 4.45 + -4.45 = 0.00 0.00 + x = -4.593745748 + -4.45 x = -4.593745748 + -4.45 Combine like terms: -4.593745748 + -4.45 = -9.043745748 x = -9.043745748 Simplifying x = -9.043745748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.143745748, -9.043745748}

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