7x^2+9x-28=0

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Solution for 7x^2+9x-28=0 equation:


Simplifying
7x2 + 9x + -28 = 0

Reorder the terms:
-28 + 9x + 7x2 = 0

Solving
-28 + 9x + 7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-4 + 1.285714286x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 1.285714286x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 1.285714286x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1.285714286x + x2 = 0 + 4
1.285714286x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
1.285714286x + x2 = 4

The x term is 1.285714286x.  Take half its coefficient (0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
1.285714286x + 0.4132653063 + x2 = 4 + 0.4132653063

Reorder the terms:
0.4132653063 + 1.285714286x + x2 = 4 + 0.4132653063

Combine like terms: 4 + 0.4132653063 = 4.4132653063
0.4132653063 + 1.285714286x + x2 = 4.4132653063

Factor a perfect square on the left side:
(x + 0.642857143)(x + 0.642857143) = 4.4132653063

Calculate the square root of the right side: 2.10077731

Break this problem into two subproblems by setting 
(x + 0.642857143) equal to 2.10077731 and -2.10077731.

Subproblem 1

x + 0.642857143 = 2.10077731 Simplifying x + 0.642857143 = 2.10077731 Reorder the terms: 0.642857143 + x = 2.10077731 Solving 0.642857143 + x = 2.10077731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = 2.10077731 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = 2.10077731 + -0.642857143 x = 2.10077731 + -0.642857143 Combine like terms: 2.10077731 + -0.642857143 = 1.457920167 x = 1.457920167 Simplifying x = 1.457920167

Subproblem 2

x + 0.642857143 = -2.10077731 Simplifying x + 0.642857143 = -2.10077731 Reorder the terms: 0.642857143 + x = -2.10077731 Solving 0.642857143 + x = -2.10077731 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + x = -2.10077731 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + x = -2.10077731 + -0.642857143 x = -2.10077731 + -0.642857143 Combine like terms: -2.10077731 + -0.642857143 = -2.743634453 x = -2.743634453 Simplifying x = -2.743634453

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.457920167, -2.743634453}

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