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Simplifying 4x2 + 2x + -2 = 14 + -14x Reorder the terms: -2 + 2x + 4x2 = 14 + -14x Solving -2 + 2x + 4x2 = 14 + -14x Solving for variable 'x'. Reorder the terms: -2 + -14 + 2x + 14x + 4x2 = 14 + -14x + -14 + 14x Combine like terms: -2 + -14 = -16 -16 + 2x + 14x + 4x2 = 14 + -14x + -14 + 14x Combine like terms: 2x + 14x = 16x -16 + 16x + 4x2 = 14 + -14x + -14 + 14x Reorder the terms: -16 + 16x + 4x2 = 14 + -14 + -14x + 14x Combine like terms: 14 + -14 = 0 -16 + 16x + 4x2 = 0 + -14x + 14x -16 + 16x + 4x2 = -14x + 14x Combine like terms: -14x + 14x = 0 -16 + 16x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 4x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + 4x + x2)' equal to zero and attempt to solve: Simplifying -4 + 4x + x2 = 0 Solving -4 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 4x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 4x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4x + x2 = 0 + 4 4x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 4x + x2 = 4 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 = 4 + 4 Reorder the terms: 4 + 4x + x2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + 4x + x2 = 8 Factor a perfect square on the left side: (x + 2)(x + 2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + 2) equal to 2.828427125 and -2.828427125.Subproblem 1
x + 2 = 2.828427125 Simplifying x + 2 = 2.828427125 Reorder the terms: 2 + x = 2.828427125 Solving 2 + x = 2.828427125 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 = 2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.828427125 + -2 x = 2.828427125 + -2 Combine like terms: 2.828427125 + -2 = 0.828427125 x = 0.828427125 Simplifying x = 0.828427125Subproblem 2
x + 2 = -2.828427125 Simplifying x + 2 = -2.828427125 Reorder the terms: 2 + x = -2.828427125 Solving 2 + x = -2.828427125 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 = -2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.828427125 + -2 x = -2.828427125 + -2 Combine like terms: -2.828427125 + -2 = -4.828427125 x = -4.828427125 Simplifying x = -4.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.828427125, -4.828427125}Solution
x = {0.828427125, -4.828427125}
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