(x+7)(x+7)=19

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Solution for (x+7)(x+7)=19 equation:


Simplifying
(x + 7)(x + 7) = 19

Reorder the terms:
(7 + x)(x + 7) = 19

Reorder the terms:
(7 + x)(7 + x) = 19

Multiply (7 + x) * (7 + x)
(7(7 + x) + x(7 + x)) = 19
((7 * 7 + x * 7) + x(7 + x)) = 19
((49 + 7x) + x(7 + x)) = 19
(49 + 7x + (7 * x + x * x)) = 19
(49 + 7x + (7x + x2)) = 19

Combine like terms: 7x + 7x = 14x
(49 + 14x + x2) = 19

Solving
49 + 14x + x2 = 19

Solving for variable 'x'.

Reorder the terms:
49 + -19 + 14x + x2 = 19 + -19

Combine like terms: 49 + -19 = 30
30 + 14x + x2 = 19 + -19

Combine like terms: 19 + -19 = 0
30 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 14x + -30 + x2 = 0 + -30

Reorder the terms:
30 + -30 + 14x + x2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 14x + x2 = 0 + -30
14x + x2 = 0 + -30

Combine like terms: 0 + -30 = -30
14x + x2 = -30

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -30 + 49

Reorder the terms:
49 + 14x + x2 = -30 + 49

Combine like terms: -30 + 49 = 19
49 + 14x + x2 = 19

Factor a perfect square on the left side:
(x + 7)(x + 7) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + 7) equal to 4.358898944 and -4.358898944.

Subproblem 1

x + 7 = 4.358898944 Simplifying x + 7 = 4.358898944 Reorder the terms: 7 + x = 4.358898944 Solving 7 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 4.358898944 + -7 Combine like terms: 7 + -7 = 0 0 + x = 4.358898944 + -7 x = 4.358898944 + -7 Combine like terms: 4.358898944 + -7 = -2.641101056 x = -2.641101056 Simplifying x = -2.641101056

Subproblem 2

x + 7 = -4.358898944 Simplifying x + 7 = -4.358898944 Reorder the terms: 7 + x = -4.358898944 Solving 7 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -4.358898944 + -7 Combine like terms: 7 + -7 = 0 0 + x = -4.358898944 + -7 x = -4.358898944 + -7 Combine like terms: -4.358898944 + -7 = -11.358898944 x = -11.358898944 Simplifying x = -11.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-2.641101056, -11.358898944}

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