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Simplifying 2x2 + -6x + -84 = 0 Reorder the terms: -84 + -6x + 2x2 = 0 Solving -84 + -6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-42 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-42 + -3x + x2)' equal to zero and attempt to solve: Simplifying -42 + -3x + x2 = 0 Solving -42 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -3x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -3x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -3x + x2 = 0 + 42 -3x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -3x + x2 = 42 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 42 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 42 + 2.25 Combine like terms: 42 + 2.25 = 44.25 2.25 + -3x + x2 = 44.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + -1.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + -1.5 = 6.652067348 Simplifying x + -1.5 = 6.652067348 Reorder the terms: -1.5 + x = 6.652067348 Solving -1.5 + x = 6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.652067348 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.652067348 + 1.5 x = 6.652067348 + 1.5 Combine like terms: 6.652067348 + 1.5 = 8.152067348 x = 8.152067348 Simplifying x = 8.152067348Subproblem 2
x + -1.5 = -6.652067348 Simplifying x + -1.5 = -6.652067348 Reorder the terms: -1.5 + x = -6.652067348 Solving -1.5 + x = -6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.652067348 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.652067348 + 1.5 x = -6.652067348 + 1.5 Combine like terms: -6.652067348 + 1.5 = -5.152067348 x = -5.152067348 Simplifying x = -5.152067348Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.152067348, -5.152067348}Solution
x = {8.152067348, -5.152067348}
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