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Simplifying 0 = 16x2 + -6x + -4 Reorder the terms: 0 = -4 + -6x + 16x2 Solving 0 = -4 + -6x + 16x2 Solving for variable 'x'. Combine like terms: 0 + 4 = 4 4 + 6x + -16x2 = -4 + -6x + 16x2 + 4 + 6x + -16x2 Reorder the terms: 4 + 6x + -16x2 = -4 + 4 + -6x + 6x + 16x2 + -16x2 Combine like terms: -4 + 4 = 0 4 + 6x + -16x2 = 0 + -6x + 6x + 16x2 + -16x2 4 + 6x + -16x2 = -6x + 6x + 16x2 + -16x2 Combine like terms: -6x + 6x = 0 4 + 6x + -16x2 = 0 + 16x2 + -16x2 4 + 6x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 4 + 6x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 3x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 3x + -8x2)' equal to zero and attempt to solve: Simplifying 2 + 3x + -8x2 = 0 Solving 2 + 3x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.25 + -0.375x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.375x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.375x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.375x + x2 = 0 + 0.25 -0.375x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.375x + x2 = 0.25 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 0.25 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 0.25 + 0.03515625 Combine like terms: 0.25 + 0.03515625 = 0.28515625 0.03515625 + -0.375x + x2 = 0.28515625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 0.28515625 Calculate the square root of the right side: 0.534000234 Break this problem into two subproblems by setting (x + -0.1875) equal to 0.534000234 and -0.534000234.Subproblem 1
x + -0.1875 = 0.534000234 Simplifying x + -0.1875 = 0.534000234 Reorder the terms: -0.1875 + x = 0.534000234 Solving -0.1875 + x = 0.534000234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 0.534000234 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 0.534000234 + 0.1875 x = 0.534000234 + 0.1875 Combine like terms: 0.534000234 + 0.1875 = 0.721500234 x = 0.721500234 Simplifying x = 0.721500234Subproblem 2
x + -0.1875 = -0.534000234 Simplifying x + -0.1875 = -0.534000234 Reorder the terms: -0.1875 + x = -0.534000234 Solving -0.1875 + x = -0.534000234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -0.534000234 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -0.534000234 + 0.1875 x = -0.534000234 + 0.1875 Combine like terms: -0.534000234 + 0.1875 = -0.346500234 x = -0.346500234 Simplifying x = -0.346500234Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.721500234, -0.346500234}Solution
x = {0.721500234, -0.346500234}
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