x=16x^2+3x-6

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Solution for x=16x^2+3x-6 equation:


Simplifying
x = 16x2 + 3x + -6

Reorder the terms:
x = -6 + 3x + 16x2

Solving
x = -6 + 3x + 16x2

Solving for variable 'x'.

Reorder the terms:
6 + x + -3x + -16x2 = -6 + 3x + 16x2 + 6 + -3x + -16x2

Combine like terms: x + -3x = -2x
6 + -2x + -16x2 = -6 + 3x + 16x2 + 6 + -3x + -16x2

Reorder the terms:
6 + -2x + -16x2 = -6 + 6 + 3x + -3x + 16x2 + -16x2

Combine like terms: -6 + 6 = 0
6 + -2x + -16x2 = 0 + 3x + -3x + 16x2 + -16x2
6 + -2x + -16x2 = 3x + -3x + 16x2 + -16x2

Combine like terms: 3x + -3x = 0
6 + -2x + -16x2 = 0 + 16x2 + -16x2
6 + -2x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
6 + -2x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -1x + -8x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -1x + -8x2)' equal to zero and attempt to solve: Simplifying 3 + -1x + -8x2 = 0 Solving 3 + -1x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + 0.125x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 0.125x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 0.125x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 0.125x + x2 = 0 + 0.375 0.125x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 0.125x + x2 = 0.375 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = 0.375 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 0.375 + 0.00390625 Combine like terms: 0.375 + 0.00390625 = 0.37890625 0.00390625 + 0.125x + x2 = 0.37890625 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 0.37890625 Calculate the square root of the right side: 0.615553613 Break this problem into two subproblems by setting (x + 0.0625) equal to 0.615553613 and -0.615553613.

Subproblem 1

x + 0.0625 = 0.615553613 Simplifying x + 0.0625 = 0.615553613 Reorder the terms: 0.0625 + x = 0.615553613 Solving 0.0625 + x = 0.615553613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = 0.615553613 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 0.615553613 + -0.0625 x = 0.615553613 + -0.0625 Combine like terms: 0.615553613 + -0.0625 = 0.553053613 x = 0.553053613 Simplifying x = 0.553053613

Subproblem 2

x + 0.0625 = -0.615553613 Simplifying x + 0.0625 = -0.615553613 Reorder the terms: 0.0625 + x = -0.615553613 Solving 0.0625 + x = -0.615553613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = -0.615553613 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -0.615553613 + -0.0625 x = -0.615553613 + -0.0625 Combine like terms: -0.615553613 + -0.0625 = -0.678053613 x = -0.678053613 Simplifying x = -0.678053613

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.553053613, -0.678053613}

Solution

x = {0.553053613, -0.678053613}

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