0=x^2+7x+3

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Solution for 0=x^2+7x+3 equation:


Simplifying
0 = x2 + 7x + 3

Reorder the terms:
0 = 3 + 7x + x2

Solving
0 = 3 + 7x + x2

Solving for variable 'x'.

Combine like terms: 0 + -3 = -3
-3 + -7x + -1x2 = 3 + 7x + x2 + -3 + -7x + -1x2

Reorder the terms:
-3 + -7x + -1x2 = 3 + -3 + 7x + -7x + x2 + -1x2

Combine like terms: 3 + -3 = 0
-3 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2
-3 + -7x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
-3 + -7x + -1x2 = 0 + x2 + -1x2
-3 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-3 + -7x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 7x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(3 + 7x + x2)' equal to zero and attempt to solve: Simplifying 3 + 7x + x2 = 0 Solving 3 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 7x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 7x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7x + x2 = 0 + -3 7x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 7x + x2 = -3 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -3 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -3 + 12.25 Combine like terms: -3 + 12.25 = 9.25 12.25 + 7x + x2 = 9.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + 3.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

x + 3.5 = 3.041381265 Simplifying x + 3.5 = 3.041381265 Reorder the terms: 3.5 + x = 3.041381265 Solving 3.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.041381265 + -3.5 x = 3.041381265 + -3.5 Combine like terms: 3.041381265 + -3.5 = -0.458618735 x = -0.458618735 Simplifying x = -0.458618735

Subproblem 2

x + 3.5 = -3.041381265 Simplifying x + 3.5 = -3.041381265 Reorder the terms: 3.5 + x = -3.041381265 Solving 3.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.041381265 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.041381265 + -3.5 x = -3.041381265 + -3.5 Combine like terms: -3.041381265 + -3.5 = -6.541381265 x = -6.541381265 Simplifying x = -6.541381265

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.458618735, -6.541381265}

Solution

x = {-0.458618735, -6.541381265}

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