# 2x*2x+1*1-3x=5

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## Solution for 2x*2x+1*1-3x=5 equation:

Simplifying
2x * 2x + 1 * 1 + -3x = 5

Reorder the terms for easier multiplication:
2 * 2x * x + 1 * 1 + -3x = 5

Multiply 2 * 2
4x * x + 1 * 1 + -3x = 5

Multiply x * x
4x2 + 1 * 1 + -3x = 5

Multiply 1 * 1
4x2 + 1 + -3x = 5

Reorder the terms:
1 + -3x + 4x2 = 5

Solving
1 + -3x + 4x2 = 5

Solving for variable 'x'.

Reorder the terms:
1 + -5 + -3x + 4x2 = 5 + -5

Combine like terms: 1 + -5 = -4
-4 + -3x + 4x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-4 + -3x + 4x2 = 0

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

Divide each side by '4'.
-1 + -0.75x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.75x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -0.75x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.75x + x2 = 0 + 1
-0.75x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-0.75x + x2 = 1

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 1 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 1 + 0.140625

Combine like terms: 1 + 0.140625 = 1.140625
0.140625 + -0.75x + x2 = 1.140625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting
(x + -0.375) equal to 1.068000468 and -1.068000468.

Subproblem 1x + -0.375 = 1.068000468

Simplifying
x + -0.375 = 1.068000468

Reorder the terms:
-0.375 + x = 1.068000468

Solving
-0.375 + x = 1.068000468

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = 1.068000468 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = 1.068000468 + 0.375
x = 1.068000468 + 0.375

Combine like terms: 1.068000468 + 0.375 = 1.443000468
x = 1.443000468

Simplifying
x = 1.443000468

Subproblem 2x + -0.375 = -1.068000468

Simplifying
x + -0.375 = -1.068000468

Reorder the terms:
-0.375 + x = -1.068000468

Solving
-0.375 + x = -1.068000468

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x = -1.068000468 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x = -1.068000468 + 0.375
x = -1.068000468 + 0.375

Combine like terms: -1.068000468 + 0.375 = -0.693000468
x = -0.693000468

Simplifying
x = -0.693000468

SolutionThe solution to the problem is based on the solutions
from the subproblems.
x = {1.443000468, -0.693000468}`