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Simplifying 4x2 + 32x + 62 = 0 Reorder the terms: 62 + 32x + 4x2 = 0 Solving 62 + 32x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(31 + 16x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(31 + 16x + 2x2)' equal to zero and attempt to solve: Simplifying 31 + 16x + 2x2 = 0 Solving 31 + 16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 15.5 + 8x + x2 = 0 Move the constant term to the right: Add '-15.5' to each side of the equation. 15.5 + 8x + -15.5 + x2 = 0 + -15.5 Reorder the terms: 15.5 + -15.5 + 8x + x2 = 0 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + 8x + x2 = 0 + -15.5 8x + x2 = 0 + -15.5 Combine like terms: 0 + -15.5 = -15.5 8x + x2 = -15.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -15.5 + 16 Reorder the terms: 16 + 8x + x2 = -15.5 + 16 Combine like terms: -15.5 + 16 = 0.5 16 + 8x + x2 = 0.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x + 4) equal to 0.707106781 and -0.707106781.Subproblem 1
x + 4 = 0.707106781 Simplifying x + 4 = 0.707106781 Reorder the terms: 4 + x = 0.707106781 Solving 4 + x = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0.707106781 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0.707106781 + -4 x = 0.707106781 + -4 Combine like terms: 0.707106781 + -4 = -3.292893219 x = -3.292893219 Simplifying x = -3.292893219Subproblem 2
x + 4 = -0.707106781 Simplifying x + 4 = -0.707106781 Reorder the terms: 4 + x = -0.707106781 Solving 4 + x = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -0.707106781 + -4 Combine like terms: 4 + -4 = 0 0 + x = -0.707106781 + -4 x = -0.707106781 + -4 Combine like terms: -0.707106781 + -4 = -4.707106781 x = -4.707106781 Simplifying x = -4.707106781Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.292893219, -4.707106781}Solution
x = {-3.292893219, -4.707106781}
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