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Simplifying 2x2 + 8x + -6 = 12 Reorder the terms: -6 + 8x + 2x2 = 12 Solving -6 + 8x + 2x2 = 12 Solving for variable 'x'. Reorder the terms: -6 + -12 + 8x + 2x2 = 12 + -12 Combine like terms: -6 + -12 = -18 -18 + 8x + 2x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -18 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 4x + x2)' equal to zero and attempt to solve: Simplifying -9 + 4x + x2 = 0 Solving -9 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 4x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 4x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4x + x2 = 0 + 9 4x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 4x + x2 = 9 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 9 + 4 Reorder the terms: 4 + 4x + x2 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + 4x + x2 = 13 Factor a perfect square on the left side: (x + 2)(x + 2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 2) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 2 = 3.605551275 Simplifying x + 2 = 3.605551275 Reorder the terms: 2 + x = 3.605551275 Solving 2 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.605551275 + -2 x = 3.605551275 + -2 Combine like terms: 3.605551275 + -2 = 1.605551275 x = 1.605551275 Simplifying x = 1.605551275Subproblem 2
x + 2 = -3.605551275 Simplifying x + 2 = -3.605551275 Reorder the terms: 2 + x = -3.605551275 Solving 2 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.605551275 + -2 x = -3.605551275 + -2 Combine like terms: -3.605551275 + -2 = -5.605551275 x = -5.605551275 Simplifying x = -5.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.605551275, -5.605551275}Solution
x = {1.605551275, -5.605551275}
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