4x^2+6x-7=0

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Solution for 4x^2+6x-7=0 equation: 


Simplifying
4x2 + 6x + -7 = 0

Reorder the terms:
-7 + 6x + 4x2 = 0

Solving
-7 + 6x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-1.75 + 1.5x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 1.5x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 1.5x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 1.5x + x2 = 0 + 1.75
1.5x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
1.5x + x2 = 1.75

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 1.75 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 1.75 + 0.5625

Combine like terms: 1.75 + 0.5625 = 2.3125
0.5625 + 1.5x + x2 = 2.3125

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 2.3125

Calculate the square root of the right side: 1.520690633

Break this problem into two subproblems by setting 
(x + 0.75) equal to 1.520690633 and -1.520690633.


Subproblem 1
x + 0.75 = 1.520690633

Simplifying
x + 0.75 = 1.520690633

Reorder the terms:
0.75 + x = 1.520690633

Solving
0.75 + x = 1.520690633

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 1.520690633 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 1.520690633 + -0.75
x = 1.520690633 + -0.75

Combine like terms: 1.520690633 + -0.75 = 0.770690633
x = 0.770690633

Simplifying
x = 0.770690633


Subproblem 2
x + 0.75 = -1.520690633

Simplifying
x + 0.75 = -1.520690633

Reorder the terms:
0.75 + x = -1.520690633

Solving
0.75 + x = -1.520690633

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -1.520690633 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -1.520690633 + -0.75
x = -1.520690633 + -0.75

Combine like terms: -1.520690633 + -0.75 = -2.270690633
x = -2.270690633

Simplifying
x = -2.270690633


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.770690633, -2.270690633}

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