-16x^2+64x+1224=0

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Solution for -16x^2+64x+1224=0 equation:


Simplifying
-16x2 + 64x + 1224 = 0

Reorder the terms:
1224 + 64x + -16x2 = 0

Solving
1224 + 64x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(153 + 8x + -2x2) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(153 + 8x + -2x2)' equal to zero and attempt to solve: Simplifying 153 + 8x + -2x2 = 0 Solving 153 + 8x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -76.5 + -4x + x2 = 0 Move the constant term to the right: Add '76.5' to each side of the equation. -76.5 + -4x + 76.5 + x2 = 0 + 76.5 Reorder the terms: -76.5 + 76.5 + -4x + x2 = 0 + 76.5 Combine like terms: -76.5 + 76.5 = 0.0 0.0 + -4x + x2 = 0 + 76.5 -4x + x2 = 0 + 76.5 Combine like terms: 0 + 76.5 = 76.5 -4x + x2 = 76.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 76.5 + 4 Reorder the terms: 4 + -4x + x2 = 76.5 + 4 Combine like terms: 76.5 + 4 = 80.5 4 + -4x + x2 = 80.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 80.5 Calculate the square root of the right side: 8.972179222 Break this problem into two subproblems by setting (x + -2) equal to 8.972179222 and -8.972179222.

Subproblem 1

x + -2 = 8.972179222 Simplifying x + -2 = 8.972179222 Reorder the terms: -2 + x = 8.972179222 Solving -2 + x = 8.972179222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 8.972179222 + 2 Combine like terms: -2 + 2 = 0 0 + x = 8.972179222 + 2 x = 8.972179222 + 2 Combine like terms: 8.972179222 + 2 = 10.972179222 x = 10.972179222 Simplifying x = 10.972179222

Subproblem 2

x + -2 = -8.972179222 Simplifying x + -2 = -8.972179222 Reorder the terms: -2 + x = -8.972179222 Solving -2 + x = -8.972179222 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -8.972179222 + 2 Combine like terms: -2 + 2 = 0 0 + x = -8.972179222 + 2 x = -8.972179222 + 2 Combine like terms: -8.972179222 + 2 = -6.972179222 x = -6.972179222 Simplifying x = -6.972179222

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.972179222, -6.972179222}

Solution

x = {10.972179222, -6.972179222}

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