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Simplifying 3(-19 + 32x + -8x2) = 0 (-19 * 3 + 32x * 3 + -8x2 * 3) = 0 (-57 + 96x + -24x2) = 0 Solving -57 + 96x + -24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-19 + 32x + -8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-19 + 32x + -8x2)' equal to zero and attempt to solve: Simplifying -19 + 32x + -8x2 = 0 Solving -19 + 32x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 2.375 + -4x + x2 = 0 Move the constant term to the right: Add '-2.375' to each side of the equation. 2.375 + -4x + -2.375 + x2 = 0 + -2.375 Reorder the terms: 2.375 + -2.375 + -4x + x2 = 0 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + -4x + x2 = 0 + -2.375 -4x + x2 = 0 + -2.375 Combine like terms: 0 + -2.375 = -2.375 -4x + x2 = -2.375 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 = -2.375 + 4 Reorder the terms: 4 + -4x + x2 = -2.375 + 4 Combine like terms: -2.375 + 4 = 1.625 4 + -4x + x2 = 1.625 Factor a perfect square on the left side: (x + -2)(x + -2) = 1.625 Calculate the square root of the right side: 1.274754878 Break this problem into two subproblems by setting (x + -2) equal to 1.274754878 and -1.274754878.Subproblem 1
x + -2 = 1.274754878 Simplifying x + -2 = 1.274754878 Reorder the terms: -2 + x = 1.274754878 Solving -2 + x = 1.274754878 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 = 1.274754878 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.274754878 + 2 x = 1.274754878 + 2 Combine like terms: 1.274754878 + 2 = 3.274754878 x = 3.274754878 Simplifying x = 3.274754878Subproblem 2
x + -2 = -1.274754878 Simplifying x + -2 = -1.274754878 Reorder the terms: -2 + x = -1.274754878 Solving -2 + x = -1.274754878 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 = -1.274754878 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.274754878 + 2 x = -1.274754878 + 2 Combine like terms: -1.274754878 + 2 = 0.725245122 x = 0.725245122 Simplifying x = 0.725245122Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.274754878, 0.725245122}Solution
x = {3.274754878, 0.725245122}
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