4x^2+28x=7

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Solution for 4x^2+28x=7 equation:


Simplifying
4x2 + 28x = 7

Reorder the terms:
28x + 4x2 = 7

Solving
28x + 4x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + 28x + 4x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 28x + 4x2 = 0

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

Divide each side by '4'.
-1.75 + 7x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 7x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 7x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 7x + x2 = 0 + 1.75
7x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
7x + x2 = 1.75

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 1.75 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 1.75 + 12.25

Combine like terms: 1.75 + 12.25 = 14
12.25 + 7x + x2 = 14

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.741657387 and -3.741657387.

Subproblem 1

x + 3.5 = 3.741657387 Simplifying x + 3.5 = 3.741657387 Reorder the terms: 3.5 + x = 3.741657387 Solving 3.5 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.741657387 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.741657387 + -3.5 x = 3.741657387 + -3.5 Combine like terms: 3.741657387 + -3.5 = 0.241657387 x = 0.241657387 Simplifying x = 0.241657387

Subproblem 2

x + 3.5 = -3.741657387 Simplifying x + 3.5 = -3.741657387 Reorder the terms: 3.5 + x = -3.741657387 Solving 3.5 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.741657387 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.741657387 + -3.5 x = -3.741657387 + -3.5 Combine like terms: -3.741657387 + -3.5 = -7.241657387 x = -7.241657387 Simplifying x = -7.241657387

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.241657387, -7.241657387}

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