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Simplifying 2x2 = 66 + -6x Solving 2x2 = 66 + -6x Solving for variable 'x'. Reorder the terms: -66 + 6x + 2x2 = 66 + -6x + -66 + 6x Reorder the terms: -66 + 6x + 2x2 = 66 + -66 + -6x + 6x Combine like terms: 66 + -66 = 0 -66 + 6x + 2x2 = 0 + -6x + 6x -66 + 6x + 2x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -66 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-33 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-33 + 3x + x2)' equal to zero and attempt to solve: Simplifying -33 + 3x + x2 = 0 Solving -33 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + 3x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + 3x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + 3x + x2 = 0 + 33 3x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 3x + x2 = 33 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 = 33 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 33 + 2.25 Combine like terms: 33 + 2.25 = 35.25 2.25 + 3x + x2 = 35.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + 1.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + 1.5 = 5.937171044 Simplifying x + 1.5 = 5.937171044 Reorder the terms: 1.5 + x = 5.937171044 Solving 1.5 + x = 5.937171044 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 = 5.937171044 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.937171044 + -1.5 x = 5.937171044 + -1.5 Combine like terms: 5.937171044 + -1.5 = 4.437171044 x = 4.437171044 Simplifying x = 4.437171044Subproblem 2
x + 1.5 = -5.937171044 Simplifying x + 1.5 = -5.937171044 Reorder the terms: 1.5 + x = -5.937171044 Solving 1.5 + x = -5.937171044 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 = -5.937171044 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.937171044 + -1.5 x = -5.937171044 + -1.5 Combine like terms: -5.937171044 + -1.5 = -7.437171044 x = -7.437171044 Simplifying x = -7.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.437171044, -7.437171044}Solution
x = {4.437171044, -7.437171044}
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