(x-7)(x-7)=98

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Solution for (x-7)(x-7)=98 equation:


Simplifying
(x + -7)(x + -7) = 98

Reorder the terms:
(-7 + x)(x + -7) = 98

Reorder the terms:
(-7 + x)(-7 + x) = 98

Multiply (-7 + x) * (-7 + x)
(-7(-7 + x) + x(-7 + x)) = 98
((-7 * -7 + x * -7) + x(-7 + x)) = 98
((49 + -7x) + x(-7 + x)) = 98
(49 + -7x + (-7 * x + x * x)) = 98
(49 + -7x + (-7x + x2)) = 98

Combine like terms: -7x + -7x = -14x
(49 + -14x + x2) = 98

Solving
49 + -14x + x2 = 98

Solving for variable 'x'.

Reorder the terms:
49 + -98 + -14x + x2 = 98 + -98

Combine like terms: 49 + -98 = -49
-49 + -14x + x2 = 98 + -98

Combine like terms: 98 + -98 = 0
-49 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -14x + 49 + x2 = 0 + 49

Reorder the terms:
-49 + 49 + -14x + x2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -14x + x2 = 0 + 49
-14x + x2 = 0 + 49

Combine like terms: 0 + 49 = 49
-14x + x2 = 49

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 = 49 + 49

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

Combine like terms: 49 + 49 = 98
49 + -14x + x2 = 98

Factor a perfect square on the left side:
(x + -7)(x + -7) = 98

Calculate the square root of the right side: 9.899494937

Break this problem into two subproblems by setting 
(x + -7) equal to 9.899494937 and -9.899494937.

Subproblem 1

x + -7 = 9.899494937 Simplifying x + -7 = 9.899494937 Reorder the terms: -7 + x = 9.899494937 Solving -7 + x = 9.899494937 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 = 9.899494937 + 7 Combine like terms: -7 + 7 = 0 0 + x = 9.899494937 + 7 x = 9.899494937 + 7 Combine like terms: 9.899494937 + 7 = 16.899494937 x = 16.899494937 Simplifying x = 16.899494937

Subproblem 2

x + -7 = -9.899494937 Simplifying x + -7 = -9.899494937 Reorder the terms: -7 + x = -9.899494937 Solving -7 + x = -9.899494937 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 = -9.899494937 + 7 Combine like terms: -7 + 7 = 0 0 + x = -9.899494937 + 7 x = -9.899494937 + 7 Combine like terms: -9.899494937 + 7 = -2.899494937 x = -2.899494937 Simplifying x = -2.899494937

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.899494937, -2.899494937}

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