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Simplifying 3x2 + -6x + -84 = 0 Reorder the terms: -84 + -6x + 3x2 = 0 Solving -84 + -6x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-28 + -2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-28 + -2x + x2)' equal to zero and attempt to solve: Simplifying -28 + -2x + x2 = 0 Solving -28 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -2x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -2x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -2x + x2 = 0 + 28 -2x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -2x + x2 = 28 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 28 + 1 Reorder the terms: 1 + -2x + x2 = 28 + 1 Combine like terms: 28 + 1 = 29 1 + -2x + x2 = 29 Factor a perfect square on the left side: (x + -1)(x + -1) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + -1) equal to 5.385164807 and -5.385164807.Subproblem 1
x + -1 = 5.385164807 Simplifying x + -1 = 5.385164807 Reorder the terms: -1 + x = 5.385164807 Solving -1 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 5.385164807 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.385164807 + 1 x = 5.385164807 + 1 Combine like terms: 5.385164807 + 1 = 6.385164807 x = 6.385164807 Simplifying x = 6.385164807Subproblem 2
x + -1 = -5.385164807 Simplifying x + -1 = -5.385164807 Reorder the terms: -1 + x = -5.385164807 Solving -1 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -5.385164807 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.385164807 + 1 x = -5.385164807 + 1 Combine like terms: -5.385164807 + 1 = -4.385164807 x = -4.385164807 Simplifying x = -4.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.385164807, -4.385164807}Solution
x = {6.385164807, -4.385164807}
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