16=4.71x+x^2

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Solution for 16=4.71x+x^2 equation:


Simplifying
16 = 4.71x + x2

Solving
16 = 4.71x + x2

Solving for variable 'x'.

Reorder the terms:
16 + -4.71x + -1x2 = 4.71x + -4.71x + x2 + -1x2

Combine like terms: 4.71x + -4.71x = 0.00
16 + -4.71x + -1x2 = 0.00 + x2 + -1x2
16 + -4.71x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + -4.71x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16 + 4.71x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 4.71x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 4.71x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 4.71x + x2 = 0 + 16
4.71x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
4.71x + x2 = 16

The x term is 4.71x.  Take half its coefficient (2.355).
Square it (5.546025) and add it to both sides.

Add '5.546025' to each side of the equation.
4.71x + 5.546025 + x2 = 16 + 5.546025

Reorder the terms:
5.546025 + 4.71x + x2 = 16 + 5.546025

Combine like terms: 16 + 5.546025 = 21.546025
5.546025 + 4.71x + x2 = 21.546025

Factor a perfect square on the left side:
(x + 2.355)(x + 2.355) = 21.546025

Calculate the square root of the right side: 4.641769598

Break this problem into two subproblems by setting 
(x + 2.355) equal to 4.641769598 and -4.641769598.

Subproblem 1

x + 2.355 = 4.641769598 Simplifying x + 2.355 = 4.641769598 Reorder the terms: 2.355 + x = 4.641769598 Solving 2.355 + x = 4.641769598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.355' to each side of the equation. 2.355 + -2.355 + x = 4.641769598 + -2.355 Combine like terms: 2.355 + -2.355 = 0.000 0.000 + x = 4.641769598 + -2.355 x = 4.641769598 + -2.355 Combine like terms: 4.641769598 + -2.355 = 2.286769598 x = 2.286769598 Simplifying x = 2.286769598

Subproblem 2

x + 2.355 = -4.641769598 Simplifying x + 2.355 = -4.641769598 Reorder the terms: 2.355 + x = -4.641769598 Solving 2.355 + x = -4.641769598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.355' to each side of the equation. 2.355 + -2.355 + x = -4.641769598 + -2.355 Combine like terms: 2.355 + -2.355 = 0.000 0.000 + x = -4.641769598 + -2.355 x = -4.641769598 + -2.355 Combine like terms: -4.641769598 + -2.355 = -6.996769598 x = -6.996769598 Simplifying x = -6.996769598

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.286769598, -6.996769598}

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