-16x^2-128x+20=0

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Solution for -16x^2-128x+20=0 equation:


Simplifying
-16x2 + -128x + 20 = 0

Reorder the terms:
20 + -128x + -16x2 = 0

Solving
20 + -128x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -32x + -4x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(5 + -32x + -4x2)' equal to zero and attempt to solve: Simplifying 5 + -32x + -4x2 = 0 Solving 5 + -32x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + 8x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 8x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 8x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 8x + x2 = 0 + 1.25 8x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 8x + x2 = 1.25 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 1.25 + 16 Reorder the terms: 16 + 8x + x2 = 1.25 + 16 Combine like terms: 1.25 + 16 = 17.25 16 + 8x + x2 = 17.25 Factor a perfect square on the left side: (x + 4)(x + 4) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + 4) equal to 4.153311931 and -4.153311931.

Subproblem 1

x + 4 = 4.153311931 Simplifying x + 4 = 4.153311931 Reorder the terms: 4 + x = 4.153311931 Solving 4 + x = 4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.153311931 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.153311931 + -4 x = 4.153311931 + -4 Combine like terms: 4.153311931 + -4 = 0.153311931 x = 0.153311931 Simplifying x = 0.153311931

Subproblem 2

x + 4 = -4.153311931 Simplifying x + 4 = -4.153311931 Reorder the terms: 4 + x = -4.153311931 Solving 4 + x = -4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.153311931 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.153311931 + -4 x = -4.153311931 + -4 Combine like terms: -4.153311931 + -4 = -8.153311931 x = -8.153311931 Simplifying x = -8.153311931

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.153311931, -8.153311931}

Solution

x = {0.153311931, -8.153311931}

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