24x^2-63x+36=0

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Solution for 24x^2-63x+36=0 equation:


Simplifying
24x2 + -63x + 36 = 0

Reorder the terms:
36 + -63x + 24x2 = 0

Solving
36 + -63x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -21x + 8x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(12 + -21x + 8x2)' equal to zero and attempt to solve: Simplifying 12 + -21x + 8x2 = 0 Solving 12 + -21x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.5 + -2.625x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2.625x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2.625x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2.625x + x2 = 0 + -1.5 -2.625x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2.625x + x2 = -1.5 The x term is -2.625x. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625x + 1.72265625 + x2 = -1.5 + 1.72265625 Reorder the terms: 1.72265625 + -2.625x + x2 = -1.5 + 1.72265625 Combine like terms: -1.5 + 1.72265625 = 0.22265625 1.72265625 + -2.625x + x2 = 0.22265625 Factor a perfect square on the left side: (x + -1.3125)(x + -1.3125) = 0.22265625 Calculate the square root of the right side: 0.471864652 Break this problem into two subproblems by setting (x + -1.3125) equal to 0.471864652 and -0.471864652.

Subproblem 1

x + -1.3125 = 0.471864652 Simplifying x + -1.3125 = 0.471864652 Reorder the terms: -1.3125 + x = 0.471864652 Solving -1.3125 + x = 0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = 0.471864652 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = 0.471864652 + 1.3125 x = 0.471864652 + 1.3125 Combine like terms: 0.471864652 + 1.3125 = 1.784364652 x = 1.784364652 Simplifying x = 1.784364652

Subproblem 2

x + -1.3125 = -0.471864652 Simplifying x + -1.3125 = -0.471864652 Reorder the terms: -1.3125 + x = -0.471864652 Solving -1.3125 + x = -0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = -0.471864652 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = -0.471864652 + 1.3125 x = -0.471864652 + 1.3125 Combine like terms: -0.471864652 + 1.3125 = 0.840635348 x = 0.840635348 Simplifying x = 0.840635348

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.784364652, 0.840635348}

Solution

x = {1.784364652, 0.840635348}

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