(4x+9)(x-7)-8x+18=0

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Solution for (4x+9)(x-7)-8x+18=0 equation:


Simplifying
(4x + 9)(x + -7) + -8x + 18 = 0

Reorder the terms:
(9 + 4x)(x + -7) + -8x + 18 = 0

Reorder the terms:
(9 + 4x)(-7 + x) + -8x + 18 = 0

Multiply (9 + 4x) * (-7 + x)
(9(-7 + x) + 4x * (-7 + x)) + -8x + 18 = 0
((-7 * 9 + x * 9) + 4x * (-7 + x)) + -8x + 18 = 0
((-63 + 9x) + 4x * (-7 + x)) + -8x + 18 = 0
(-63 + 9x + (-7 * 4x + x * 4x)) + -8x + 18 = 0
(-63 + 9x + (-28x + 4x2)) + -8x + 18 = 0

Combine like terms: 9x + -28x = -19x
(-63 + -19x + 4x2) + -8x + 18 = 0

Reorder the terms:
-63 + 18 + -19x + -8x + 4x2 = 0

Combine like terms: -63 + 18 = -45
-45 + -19x + -8x + 4x2 = 0

Combine like terms: -19x + -8x = -27x
-45 + -27x + 4x2 = 0

Solving
-45 + -27x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-11.25 + -6.75x + x2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + -6.75x + 11.25 + x2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + -6.75x + x2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + -6.75x + x2 = 0 + 11.25
-6.75x + x2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
-6.75x + x2 = 11.25

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = 11.25 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = 11.25 + 11.390625

Combine like terms: 11.25 + 11.390625 = 22.640625
11.390625 + -6.75x + x2 = 22.640625

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = 22.640625

Calculate the square root of the right side: 4.758216578

Break this problem into two subproblems by setting 
(x + -3.375) equal to 4.758216578 and -4.758216578.

Subproblem 1

x + -3.375 = 4.758216578 Simplifying x + -3.375 = 4.758216578 Reorder the terms: -3.375 + x = 4.758216578 Solving -3.375 + x = 4.758216578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 4.758216578 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 4.758216578 + 3.375 x = 4.758216578 + 3.375 Combine like terms: 4.758216578 + 3.375 = 8.133216578 x = 8.133216578 Simplifying x = 8.133216578

Subproblem 2

x + -3.375 = -4.758216578 Simplifying x + -3.375 = -4.758216578 Reorder the terms: -3.375 + x = -4.758216578 Solving -3.375 + x = -4.758216578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -4.758216578 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -4.758216578 + 3.375 x = -4.758216578 + 3.375 Combine like terms: -4.758216578 + 3.375 = -1.383216578 x = -1.383216578 Simplifying x = -1.383216578

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.133216578, -1.383216578}

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