18x(8x-7)=67

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Solution for 18x(8x-7)=67 equation:


Simplifying
18x(8x + -7) = 67

Reorder the terms:
18x(-7 + 8x) = 67
(-7 * 18x + 8x * 18x) = 67
(-126x + 144x2) = 67

Solving
-126x + 144x2 = 67

Solving for variable 'x'.

Reorder the terms:
-67 + -126x + 144x2 = 67 + -67

Combine like terms: 67 + -67 = 0
-67 + -126x + 144x2 = 0

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

Divide each side by '144'.
-0.4652777778 + -0.875x + x2 = 0

Move the constant term to the right:

Add '0.4652777778' to each side of the equation.
-0.4652777778 + -0.875x + 0.4652777778 + x2 = 0 + 0.4652777778

Reorder the terms:
-0.4652777778 + 0.4652777778 + -0.875x + x2 = 0 + 0.4652777778

Combine like terms: -0.4652777778 + 0.4652777778 = 0.0000000000
0.0000000000 + -0.875x + x2 = 0 + 0.4652777778
-0.875x + x2 = 0 + 0.4652777778

Combine like terms: 0 + 0.4652777778 = 0.4652777778
-0.875x + x2 = 0.4652777778

The x term is -0.875x.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875x + 0.19140625 + x2 = 0.4652777778 + 0.19140625

Reorder the terms:
0.19140625 + -0.875x + x2 = 0.4652777778 + 0.19140625

Combine like terms: 0.4652777778 + 0.19140625 = 0.6566840278
0.19140625 + -0.875x + x2 = 0.6566840278

Factor a perfect square on the left side:
(x + -0.4375)(x + -0.4375) = 0.6566840278

Calculate the square root of the right side: 0.810360431

Break this problem into two subproblems by setting 
(x + -0.4375) equal to 0.810360431 and -0.810360431.

Subproblem 1

x + -0.4375 = 0.810360431 Simplifying x + -0.4375 = 0.810360431 Reorder the terms: -0.4375 + x = 0.810360431 Solving -0.4375 + x = 0.810360431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 0.810360431 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 0.810360431 + 0.4375 x = 0.810360431 + 0.4375 Combine like terms: 0.810360431 + 0.4375 = 1.247860431 x = 1.247860431 Simplifying x = 1.247860431

Subproblem 2

x + -0.4375 = -0.810360431 Simplifying x + -0.4375 = -0.810360431 Reorder the terms: -0.4375 + x = -0.810360431 Solving -0.4375 + x = -0.810360431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -0.810360431 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -0.810360431 + 0.4375 x = -0.810360431 + 0.4375 Combine like terms: -0.810360431 + 0.4375 = -0.372860431 x = -0.372860431 Simplifying x = -0.372860431

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.247860431, -0.372860431}

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