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Simplifying 3x2 + 5x + -6 = x2 + x + 8 Reorder the terms: -6 + 5x + 3x2 = x2 + x + 8 Reorder the terms: -6 + 5x + 3x2 = 8 + x + x2 Solving -6 + 5x + 3x2 = 8 + x + x2 Solving for variable 'x'. Reorder the terms: -6 + -8 + 5x + -1x + 3x2 + -1x2 = 8 + x + x2 + -8 + -1x + -1x2 Combine like terms: -6 + -8 = -14 -14 + 5x + -1x + 3x2 + -1x2 = 8 + x + x2 + -8 + -1x + -1x2 Combine like terms: 5x + -1x = 4x -14 + 4x + 3x2 + -1x2 = 8 + x + x2 + -8 + -1x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -14 + 4x + 2x2 = 8 + x + x2 + -8 + -1x + -1x2 Reorder the terms: -14 + 4x + 2x2 = 8 + -8 + x + -1x + x2 + -1x2 Combine like terms: 8 + -8 = 0 -14 + 4x + 2x2 = 0 + x + -1x + x2 + -1x2 -14 + 4x + 2x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 -14 + 4x + 2x2 = 0 + x2 + -1x2 -14 + 4x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -14 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 2x + x2)' equal to zero and attempt to solve: Simplifying -7 + 2x + x2 = 0 Solving -7 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 2x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 2x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2x + x2 = 0 + 7 2x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 2x + x2 = 7 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 7 + 1 Reorder the terms: 1 + 2x + x2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + 2x + x2 = 8 Factor a perfect square on the left side: (x + 1)(x + 1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + 1) equal to 2.828427125 and -2.828427125.Subproblem 1
x + 1 = 2.828427125 Simplifying x + 1 = 2.828427125 Reorder the terms: 1 + x = 2.828427125 Solving 1 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.828427125 + -1 x = 2.828427125 + -1 Combine like terms: 2.828427125 + -1 = 1.828427125 x = 1.828427125 Simplifying x = 1.828427125Subproblem 2
x + 1 = -2.828427125 Simplifying x + 1 = -2.828427125 Reorder the terms: 1 + x = -2.828427125 Solving 1 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.828427125 + -1 x = -2.828427125 + -1 Combine like terms: -2.828427125 + -1 = -3.828427125 x = -3.828427125 Simplifying x = -3.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.828427125, -3.828427125}Solution
x = {1.828427125, -3.828427125}
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