X(4X+5)-3=5

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Solution for X(4X+5)-3=5 equation:


Simplifying
X(4X + 5) + -3 = 5

Reorder the terms:
X(5 + 4X) + -3 = 5
(5 * X + 4X * X) + -3 = 5
(5X + 4X2) + -3 = 5

Reorder the terms:
-3 + 5X + 4X2 = 5

Solving
-3 + 5X + 4X2 = 5

Solving for variable 'X'.

Reorder the terms:
-3 + -5 + 5X + 4X2 = 5 + -5

Combine like terms: -3 + -5 = -8
-8 + 5X + 4X2 = 5 + -5

Combine like terms: 5 + -5 = 0
-8 + 5X + 4X2 = 0

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

Divide each side by '4'.
-2 + 1.25X + X2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 1.25X + 2 + X2 = 0 + 2

Reorder the terms:
-2 + 2 + 1.25X + X2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 1.25X + X2 = 0 + 2
1.25X + X2 = 0 + 2

Combine like terms: 0 + 2 = 2
1.25X + X2 = 2

The X term is 1.25X.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25X + 0.390625 + X2 = 2 + 0.390625

Reorder the terms:
0.390625 + 1.25X + X2 = 2 + 0.390625

Combine like terms: 2 + 0.390625 = 2.390625
0.390625 + 1.25X + X2 = 2.390625

Factor a perfect square on the left side:
(X + 0.625)(X + 0.625) = 2.390625

Calculate the square root of the right side: 1.54616461

Break this problem into two subproblems by setting 
(X + 0.625) equal to 1.54616461 and -1.54616461.

Subproblem 1

X + 0.625 = 1.54616461 Simplifying X + 0.625 = 1.54616461 Reorder the terms: 0.625 + X = 1.54616461 Solving 0.625 + X = 1.54616461 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + X = 1.54616461 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + X = 1.54616461 + -0.625 X = 1.54616461 + -0.625 Combine like terms: 1.54616461 + -0.625 = 0.92116461 X = 0.92116461 Simplifying X = 0.92116461

Subproblem 2

X + 0.625 = -1.54616461 Simplifying X + 0.625 = -1.54616461 Reorder the terms: 0.625 + X = -1.54616461 Solving 0.625 + X = -1.54616461 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + X = -1.54616461 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + X = -1.54616461 + -0.625 X = -1.54616461 + -0.625 Combine like terms: -1.54616461 + -0.625 = -2.17116461 X = -2.17116461 Simplifying X = -2.17116461

Solution

The solution to the problem is based on the solutions from the subproblems. X = {0.92116461, -2.17116461}

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