x*x-14x+42=0

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Solution for x*x-14x+42=0 equation:


Simplifying
x * x + -14x + 42 = 0

Multiply x * x
x2 + -14x + 42 = 0

Reorder the terms:
42 + -14x + x2 = 0

Solving
42 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + -14x + -42 + x2 = 0 + -42

Reorder the terms:
42 + -42 + -14x + x2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -14x + x2 = 0 + -42
-14x + x2 = 0 + -42

Combine like terms: 0 + -42 = -42
-14x + x2 = -42

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 = -42 + 49

Reorder the terms:
49 + -14x + x2 = -42 + 49

Combine like terms: -42 + 49 = 7
49 + -14x + x2 = 7

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

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -7) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + -7 = 2.645751311 Simplifying x + -7 = 2.645751311 Reorder the terms: -7 + x = 2.645751311 Solving -7 + x = 2.645751311 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 = 2.645751311 + 7 Combine like terms: -7 + 7 = 0 0 + x = 2.645751311 + 7 x = 2.645751311 + 7 Combine like terms: 2.645751311 + 7 = 9.645751311 x = 9.645751311 Simplifying x = 9.645751311

Subproblem 2

x + -7 = -2.645751311 Simplifying x + -7 = -2.645751311 Reorder the terms: -7 + x = -2.645751311 Solving -7 + x = -2.645751311 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 = -2.645751311 + 7 Combine like terms: -7 + 7 = 0 0 + x = -2.645751311 + 7 x = -2.645751311 + 7 Combine like terms: -2.645751311 + 7 = 4.354248689 x = 4.354248689 Simplifying x = 4.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.645751311, 4.354248689}

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