-16x^2-24x=2

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Solution for -16x^2-24x=2 equation:


Simplifying
-16x2 + -24x = 2

Reorder the terms:
-24x + -16x2 = 2

Solving
-24x + -16x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + -24x + -16x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -24x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 12x + 8x2) = 0

Ignore the factor -2.

Subproblem 1

Set the factor '(1 + 12x + 8x2)' equal to zero and attempt to solve: Simplifying 1 + 12x + 8x2 = 0 Solving 1 + 12x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + 1.5x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + 1.5x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + 1.5x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + 1.5x + x2 = 0 + -0.125 1.5x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 1.5x + x2 = -0.125 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -0.125 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -0.125 + 0.5625 Combine like terms: -0.125 + 0.5625 = 0.4375 0.5625 + 1.5x + x2 = 0.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 0.4375 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (x + 0.75) equal to 0.661437828 and -0.661437828.

Subproblem 1

x + 0.75 = 0.661437828 Simplifying x + 0.75 = 0.661437828 Reorder the terms: 0.75 + x = 0.661437828 Solving 0.75 + x = 0.661437828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 0.661437828 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.661437828 + -0.75 x = 0.661437828 + -0.75 Combine like terms: 0.661437828 + -0.75 = -0.088562172 x = -0.088562172 Simplifying x = -0.088562172

Subproblem 2

x + 0.75 = -0.661437828 Simplifying x + 0.75 = -0.661437828 Reorder the terms: 0.75 + x = -0.661437828 Solving 0.75 + x = -0.661437828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -0.661437828 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.661437828 + -0.75 x = -0.661437828 + -0.75 Combine like terms: -0.661437828 + -0.75 = -1.411437828 x = -1.411437828 Simplifying x = -1.411437828

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.088562172, -1.411437828}

Solution

x = {-0.088562172, -1.411437828}

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