0=-16x^2+192x+144

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Solution for 0=-16x^2+192x+144 equation:


Simplifying
0 = -16x2 + 192x + 144

Reorder the terms:
0 = 144 + 192x + -16x2

Solving
0 = 144 + 192x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -144 = -144
-144 + -192x + 16x2 = 144 + 192x + -16x2 + -144 + -192x + 16x2

Reorder the terms:
-144 + -192x + 16x2 = 144 + -144 + 192x + -192x + -16x2 + 16x2

Combine like terms: 144 + -144 = 0
-144 + -192x + 16x2 = 0 + 192x + -192x + -16x2 + 16x2
-144 + -192x + 16x2 = 192x + -192x + -16x2 + 16x2

Combine like terms: 192x + -192x = 0
-144 + -192x + 16x2 = 0 + -16x2 + 16x2
-144 + -192x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-144 + -192x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-9 + -12x + x2) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-9 + -12x + x2)' equal to zero and attempt to solve: Simplifying -9 + -12x + x2 = 0 Solving -9 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -12x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -12x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -12x + x2 = 0 + 9 -12x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -12x + x2 = 9 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 9 + 36 Reorder the terms: 36 + -12x + x2 = 9 + 36 Combine like terms: 9 + 36 = 45 36 + -12x + x2 = 45 Factor a perfect square on the left side: (x + -6)(x + -6) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -6) equal to 6.708203933 and -6.708203933.

Subproblem 1

x + -6 = 6.708203933 Simplifying x + -6 = 6.708203933 Reorder the terms: -6 + x = 6.708203933 Solving -6 + x = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 6.708203933 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.708203933 + 6 x = 6.708203933 + 6 Combine like terms: 6.708203933 + 6 = 12.708203933 x = 12.708203933 Simplifying x = 12.708203933

Subproblem 2

x + -6 = -6.708203933 Simplifying x + -6 = -6.708203933 Reorder the terms: -6 + x = -6.708203933 Solving -6 + x = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -6.708203933 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.708203933 + 6 x = -6.708203933 + 6 Combine like terms: -6.708203933 + 6 = -0.708203933 x = -0.708203933 Simplifying x = -0.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.708203933, -0.708203933}

Solution

x = {12.708203933, -0.708203933}

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