7-4x(2x+5)=4

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Solution for 7-4x(2x+5)=4 equation:


Simplifying
7 + -4x(2x + 5) = 4

Reorder the terms:
7 + -4x(5 + 2x) = 4
7 + (5 * -4x + 2x * -4x) = 4
7 + (-20x + -8x2) = 4

Solving
7 + -20x + -8x2 = 4

Solving for variable 'x'.

Reorder the terms:
7 + -4 + -20x + -8x2 = 4 + -4

Combine like terms: 7 + -4 = 3
3 + -20x + -8x2 = 4 + -4

Combine like terms: 4 + -4 = 0
3 + -20x + -8x2 = 0

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

Divide each side by '-8'.
-0.375 + 2.5x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + 2.5x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + 2.5x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + 2.5x + x2 = 0 + 0.375
2.5x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
2.5x + x2 = 0.375

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 0.375 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 0.375 + 1.5625

Combine like terms: 0.375 + 1.5625 = 1.9375
1.5625 + 2.5x + x2 = 1.9375

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 1.9375

Calculate the square root of the right side: 1.391941091

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.391941091 and -1.391941091.

Subproblem 1

x + 1.25 = 1.391941091 Simplifying x + 1.25 = 1.391941091 Reorder the terms: 1.25 + x = 1.391941091 Solving 1.25 + x = 1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.391941091 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.391941091 + -1.25 x = 1.391941091 + -1.25 Combine like terms: 1.391941091 + -1.25 = 0.141941091 x = 0.141941091 Simplifying x = 0.141941091

Subproblem 2

x + 1.25 = -1.391941091 Simplifying x + 1.25 = -1.391941091 Reorder the terms: 1.25 + x = -1.391941091 Solving 1.25 + x = -1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.391941091 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.391941091 + -1.25 x = -1.391941091 + -1.25 Combine like terms: -1.391941091 + -1.25 = -2.641941091 x = -2.641941091 Simplifying x = -2.641941091

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.141941091, -2.641941091}

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