0=x^2+14x+16

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Solution for 0=x^2+14x+16 equation:


Simplifying
0 = x2 + 14x + 16

Reorder the terms:
0 = 16 + 14x + x2

Solving
0 = 16 + 14x + x2

Solving for variable 'x'.

Combine like terms: 0 + -16 = -16
-16 + -14x + -1x2 = 16 + 14x + x2 + -16 + -14x + -1x2

Reorder the terms:
-16 + -14x + -1x2 = 16 + -16 + 14x + -14x + x2 + -1x2

Combine like terms: 16 + -16 = 0
-16 + -14x + -1x2 = 0 + 14x + -14x + x2 + -1x2
-16 + -14x + -1x2 = 14x + -14x + x2 + -1x2

Combine like terms: 14x + -14x = 0
-16 + -14x + -1x2 = 0 + x2 + -1x2
-16 + -14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-16 + -14x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 14x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(16 + 14x + x2)' equal to zero and attempt to solve: Simplifying 16 + 14x + x2 = 0 Solving 16 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 14x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 14x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 14x + x2 = 0 + -16 14x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 14x + x2 = -16 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 = -16 + 49 Reorder the terms: 49 + 14x + x2 = -16 + 49 Combine like terms: -16 + 49 = 33 49 + 14x + x2 = 33 Factor a perfect square on the left side: (x + 7)(x + 7) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + 7) equal to 5.744562647 and -5.744562647.

Subproblem 1

x + 7 = 5.744562647 Simplifying x + 7 = 5.744562647 Reorder the terms: 7 + x = 5.744562647 Solving 7 + x = 5.744562647 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 = 5.744562647 + -7 Combine like terms: 7 + -7 = 0 0 + x = 5.744562647 + -7 x = 5.744562647 + -7 Combine like terms: 5.744562647 + -7 = -1.255437353 x = -1.255437353 Simplifying x = -1.255437353

Subproblem 2

x + 7 = -5.744562647 Simplifying x + 7 = -5.744562647 Reorder the terms: 7 + x = -5.744562647 Solving 7 + x = -5.744562647 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 = -5.744562647 + -7 Combine like terms: 7 + -7 = 0 0 + x = -5.744562647 + -7 x = -5.744562647 + -7 Combine like terms: -5.744562647 + -7 = -12.744562647 x = -12.744562647 Simplifying x = -12.744562647

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.255437353, -12.744562647}

Solution

x = {-1.255437353, -12.744562647}

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