2x(4x+7)=3

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Solution for 2x(4x+7)=3 equation:


Simplifying
2x(4x + 7) = 3

Reorder the terms:
2x(7 + 4x) = 3
(7 * 2x + 4x * 2x) = 3
(14x + 8x2) = 3

Solving
14x + 8x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 14x + 8x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 14x + 8x2 = 0

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

Divide each side by '8'.
-0.375 + 1.75x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + 1.75x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + 1.75x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + 1.75x + x2 = 0 + 0.375
1.75x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
1.75x + x2 = 0.375

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = 0.375 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 0.375 + 0.765625

Combine like terms: 0.375 + 0.765625 = 1.140625
0.765625 + 1.75x + x2 = 1.140625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(x + 0.875) equal to 1.068000468 and -1.068000468.

Subproblem 1

x + 0.875 = 1.068000468 Simplifying x + 0.875 = 1.068000468 Reorder the terms: 0.875 + x = 1.068000468 Solving 0.875 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.068000468 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.068000468 + -0.875 x = 1.068000468 + -0.875 Combine like terms: 1.068000468 + -0.875 = 0.193000468 x = 0.193000468 Simplifying x = 0.193000468

Subproblem 2

x + 0.875 = -1.068000468 Simplifying x + 0.875 = -1.068000468 Reorder the terms: 0.875 + x = -1.068000468 Solving 0.875 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.068000468 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.068000468 + -0.875 x = -1.068000468 + -0.875 Combine like terms: -1.068000468 + -0.875 = -1.943000468 x = -1.943000468 Simplifying x = -1.943000468

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.193000468, -1.943000468}

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