0=-x^2+14x+45

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Solution for 0=-x^2+14x+45 equation:


Simplifying
0 = -1x2 + 14x + 45

Reorder the terms:
0 = 45 + 14x + -1x2

Solving
0 = 45 + 14x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -45 = -45
-45 + -14x + x2 = 45 + 14x + -1x2 + -45 + -14x + x2

Reorder the terms:
-45 + -14x + x2 = 45 + -45 + 14x + -14x + -1x2 + x2

Combine like terms: 45 + -45 = 0
-45 + -14x + x2 = 0 + 14x + -14x + -1x2 + x2
-45 + -14x + x2 = 14x + -14x + -1x2 + x2

Combine like terms: 14x + -14x = 0
-45 + -14x + x2 = 0 + -1x2 + x2
-45 + -14x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-45 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -14x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + -14x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -14x + x2 = 0 + 45
-14x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
-14x + x2 = 45

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 = 45 + 49

Reorder the terms:
49 + -14x + x2 = 45 + 49

Combine like terms: 45 + 49 = 94
49 + -14x + x2 = 94

Factor a perfect square on the left side:
(x + -7)(x + -7) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(x + -7) equal to 9.695359715 and -9.695359715.

Subproblem 1

x + -7 = 9.695359715 Simplifying x + -7 = 9.695359715 Reorder the terms: -7 + x = 9.695359715 Solving -7 + x = 9.695359715 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 = 9.695359715 + 7 Combine like terms: -7 + 7 = 0 0 + x = 9.695359715 + 7 x = 9.695359715 + 7 Combine like terms: 9.695359715 + 7 = 16.695359715 x = 16.695359715 Simplifying x = 16.695359715

Subproblem 2

x + -7 = -9.695359715 Simplifying x + -7 = -9.695359715 Reorder the terms: -7 + x = -9.695359715 Solving -7 + x = -9.695359715 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 = -9.695359715 + 7 Combine like terms: -7 + 7 = 0 0 + x = -9.695359715 + 7 x = -9.695359715 + 7 Combine like terms: -9.695359715 + 7 = -2.695359715 x = -2.695359715 Simplifying x = -2.695359715

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.695359715, -2.695359715}

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