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Simplifying 2x2 + -7x = 14 + -11x Reorder the terms: -7x + 2x2 = 14 + -11x Solving -7x + 2x2 = 14 + -11x Solving for variable 'x'. Reorder the terms: -14 + -7x + 11x + 2x2 = 14 + -11x + -14 + 11x Combine like terms: -7x + 11x = 4x -14 + 4x + 2x2 = 14 + -11x + -14 + 11x Reorder the terms: -14 + 4x + 2x2 = 14 + -14 + -11x + 11x Combine like terms: 14 + -14 = 0 -14 + 4x + 2x2 = 0 + -11x + 11x -14 + 4x + 2x2 = -11x + 11x Combine like terms: -11x + 11x = 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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