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Simplifying 7 + -2x2 = 8x + 14 Reorder the terms: 7 + -2x2 = 14 + 8x Solving 7 + -2x2 = 14 + 8x Solving for variable 'x'. Reorder the terms: 7 + -14 + -8x + -2x2 = 14 + 8x + -14 + -8x Combine like terms: 7 + -14 = -7 -7 + -8x + -2x2 = 14 + 8x + -14 + -8x Reorder the terms: -7 + -8x + -2x2 = 14 + -14 + 8x + -8x Combine like terms: 14 + -14 = 0 -7 + -8x + -2x2 = 0 + 8x + -8x -7 + -8x + -2x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -7 + -8x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 8x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 8x + 2x2)' equal to zero and attempt to solve: Simplifying 7 + 8x + 2x2 = 0 Solving 7 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 4x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 4x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 4x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 4x + x2 = 0 + -3.5 4x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 4x + x2 = -3.5 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 = -3.5 + 4 Reorder the terms: 4 + 4x + x2 = -3.5 + 4 Combine like terms: -3.5 + 4 = 0.5 4 + 4x + x2 = 0.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + 2) equal to 0.707106781 and -0.707106781.Subproblem 1
x + 2 = 0.707106781 Simplifying x + 2 = 0.707106781 Reorder the terms: 2 + x = 0.707106781 Solving 2 + x = 0.707106781 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 = 0.707106781 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.707106781 + -2 x = 0.707106781 + -2 Combine like terms: 0.707106781 + -2 = -1.292893219 x = -1.292893219 Simplifying x = -1.292893219Subproblem 2
x + 2 = -0.707106781 Simplifying x + 2 = -0.707106781 Reorder the terms: 2 + x = -0.707106781 Solving 2 + x = -0.707106781 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 = -0.707106781 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.707106781 + -2 x = -0.707106781 + -2 Combine like terms: -0.707106781 + -2 = -2.707106781 x = -2.707106781 Simplifying x = -2.707106781Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.292893219, -2.707106781}Solution
x = {-1.292893219, -2.707106781}
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