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Simplifying 8x2 + 32x + 4 = 0 Reorder the terms: 4 + 32x + 8x2 = 0 Solving 4 + 32x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 8x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 8x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + 8x + 2x2 = 0 Solving 1 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + 4x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 4x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 4x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 4x + x2 = 0 + -0.5 4x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 4x + x2 = -0.5 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 = -0.5 + 4 Reorder the terms: 4 + 4x + x2 = -0.5 + 4 Combine like terms: -0.5 + 4 = 3.5 4 + 4x + x2 = 3.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (x + 2) equal to 1.870828693 and -1.870828693.Subproblem 1
x + 2 = 1.870828693 Simplifying x + 2 = 1.870828693 Reorder the terms: 2 + x = 1.870828693 Solving 2 + x = 1.870828693 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 = 1.870828693 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.870828693 + -2 x = 1.870828693 + -2 Combine like terms: 1.870828693 + -2 = -0.129171307 x = -0.129171307 Simplifying x = -0.129171307Subproblem 2
x + 2 = -1.870828693 Simplifying x + 2 = -1.870828693 Reorder the terms: 2 + x = -1.870828693 Solving 2 + x = -1.870828693 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 = -1.870828693 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.870828693 + -2 x = -1.870828693 + -2 Combine like terms: -1.870828693 + -2 = -3.870828693 x = -3.870828693 Simplifying x = -3.870828693Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.129171307, -3.870828693}Solution
x = {-0.129171307, -3.870828693}
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