14x(x-3)-22x=-18

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Solution for 14x(x-3)-22x=-18 equation:


Simplifying
14x(x + -3) + -22x = -18

Reorder the terms:
14x(-3 + x) + -22x = -18
(-3 * 14x + x * 14x) + -22x = -18
(-42x + 14x2) + -22x = -18

Reorder the terms:
-42x + -22x + 14x2 = -18

Combine like terms: -42x + -22x = -64x
-64x + 14x2 = -18

Solving
-64x + 14x2 = -18

Solving for variable 'x'.

Reorder the terms:
18 + -64x + 14x2 = -18 + 18

Combine like terms: -18 + 18 = 0
18 + -64x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -32x + 7x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(9 + -32x + 7x2)' equal to zero and attempt to solve: Simplifying 9 + -32x + 7x2 = 0 Solving 9 + -32x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.285714286 + -4.571428571x + x2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + -4.571428571x + -1.285714286 + x2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + -4.571428571x + x2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + -4.571428571x + x2 = 0 + -1.285714286 -4.571428571x + x2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 -4.571428571x + x2 = -1.285714286 The x term is -4.571428571x. Take half its coefficient (-2.285714286). Square it (5.224489797) and add it to both sides. Add '5.224489797' to each side of the equation. -4.571428571x + 5.224489797 + x2 = -1.285714286 + 5.224489797 Reorder the terms: 5.224489797 + -4.571428571x + x2 = -1.285714286 + 5.224489797 Combine like terms: -1.285714286 + 5.224489797 = 3.938775511 5.224489797 + -4.571428571x + x2 = 3.938775511 Factor a perfect square on the left side: (x + -2.285714286)(x + -2.285714286) = 3.938775511 Calculate the square root of the right side: 1.984634856 Break this problem into two subproblems by setting (x + -2.285714286) equal to 1.984634856 and -1.984634856.

Subproblem 1

x + -2.285714286 = 1.984634856 Simplifying x + -2.285714286 = 1.984634856 Reorder the terms: -2.285714286 + x = 1.984634856 Solving -2.285714286 + x = 1.984634856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.285714286' to each side of the equation. -2.285714286 + 2.285714286 + x = 1.984634856 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + x = 1.984634856 + 2.285714286 x = 1.984634856 + 2.285714286 Combine like terms: 1.984634856 + 2.285714286 = 4.270349142 x = 4.270349142 Simplifying x = 4.270349142

Subproblem 2

x + -2.285714286 = -1.984634856 Simplifying x + -2.285714286 = -1.984634856 Reorder the terms: -2.285714286 + x = -1.984634856 Solving -2.285714286 + x = -1.984634856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.285714286' to each side of the equation. -2.285714286 + 2.285714286 + x = -1.984634856 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + x = -1.984634856 + 2.285714286 x = -1.984634856 + 2.285714286 Combine like terms: -1.984634856 + 2.285714286 = 0.30107943 x = 0.30107943 Simplifying x = 0.30107943

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.270349142, 0.30107943}

Solution

x = {4.270349142, 0.30107943}

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