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Simplifying 0 = -3x2 + 24x + -42 Reorder the terms: 0 = -42 + 24x + -3x2 Solving 0 = -42 + 24x + -3x2 Solving for variable 'x'. Combine like terms: 0 + 42 = 42 42 + -24x + 3x2 = -42 + 24x + -3x2 + 42 + -24x + 3x2 Reorder the terms: 42 + -24x + 3x2 = -42 + 42 + 24x + -24x + -3x2 + 3x2 Combine like terms: -42 + 42 = 0 42 + -24x + 3x2 = 0 + 24x + -24x + -3x2 + 3x2 42 + -24x + 3x2 = 24x + -24x + -3x2 + 3x2 Combine like terms: 24x + -24x = 0 42 + -24x + 3x2 = 0 + -3x2 + 3x2 42 + -24x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 42 + -24x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(14 + -8x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(14 + -8x + x2)' equal to zero and attempt to solve: Simplifying 14 + -8x + x2 = 0 Solving 14 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -8x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -8x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -8x + x2 = 0 + -14 -8x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -8x + x2 = -14 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 = -14 + 16 Reorder the terms: 16 + -8x + x2 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + -8x + x2 = 2 Factor a perfect square on the left side: (x + -4)(x + -4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -4) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -4 = 1.414213562 Simplifying x + -4 = 1.414213562 Reorder the terms: -4 + x = 1.414213562 Solving -4 + x = 1.414213562 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 = 1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.414213562 + 4 x = 1.414213562 + 4 Combine like terms: 1.414213562 + 4 = 5.414213562 x = 5.414213562 Simplifying x = 5.414213562Subproblem 2
x + -4 = -1.414213562 Simplifying x + -4 = -1.414213562 Reorder the terms: -4 + x = -1.414213562 Solving -4 + x = -1.414213562 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 = -1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.414213562 + 4 x = -1.414213562 + 4 Combine like terms: -1.414213562 + 4 = 2.585786438 x = 2.585786438 Simplifying x = 2.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.414213562, 2.585786438}Solution
x = {5.414213562, 2.585786438}
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