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Simplifying x + 3x + -3 + 2x2 + 8x + -5 = 0 Reorder the terms: -3 + -5 + x + 3x + 8x + 2x2 = 0 Combine like terms: -3 + -5 = -8 -8 + x + 3x + 8x + 2x2 = 0 Combine like terms: x + 3x = 4x -8 + 4x + 8x + 2x2 = 0 Combine like terms: 4x + 8x = 12x -8 + 12x + 2x2 = 0 Solving -8 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 6x + x2)' equal to zero and attempt to solve: Simplifying -4 + 6x + x2 = 0 Solving -4 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 6x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 6x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6x + x2 = 0 + 4 6x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 6x + x2 = 4 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 4 + 9 Reorder the terms: 9 + 6x + x2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + 6x + x2 = 13 Factor a perfect square on the left side: (x + 3)(x + 3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 3) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 3 = 3.605551275 Simplifying x + 3 = 3.605551275 Reorder the terms: 3 + x = 3.605551275 Solving 3 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.605551275 + -3 x = 3.605551275 + -3 Combine like terms: 3.605551275 + -3 = 0.605551275 x = 0.605551275 Simplifying x = 0.605551275Subproblem 2
x + 3 = -3.605551275 Simplifying x + 3 = -3.605551275 Reorder the terms: 3 + x = -3.605551275 Solving 3 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.605551275 + -3 x = -3.605551275 + -3 Combine like terms: -3.605551275 + -3 = -6.605551275 x = -6.605551275 Simplifying x = -6.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.605551275, -6.605551275}Solution
x = {0.605551275, -6.605551275}
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