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Simplifying 4x2 + 16x + -34 = 0 Reorder the terms: -34 + 16x + 4x2 = 0 Solving -34 + 16x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-17 + 8x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + 8x + 2x2)' equal to zero and attempt to solve: Simplifying -17 + 8x + 2x2 = 0 Solving -17 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + 4x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + 4x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + 4x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + 4x + x2 = 0 + 8.5 4x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 4x + x2 = 8.5 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 = 8.5 + 4 Reorder the terms: 4 + 4x + x2 = 8.5 + 4 Combine like terms: 8.5 + 4 = 12.5 4 + 4x + x2 = 12.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + 2) equal to 3.535533906 and -3.535533906.Subproblem 1
x + 2 = 3.535533906 Simplifying x + 2 = 3.535533906 Reorder the terms: 2 + x = 3.535533906 Solving 2 + x = 3.535533906 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 = 3.535533906 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.535533906 + -2 x = 3.535533906 + -2 Combine like terms: 3.535533906 + -2 = 1.535533906 x = 1.535533906 Simplifying x = 1.535533906Subproblem 2
x + 2 = -3.535533906 Simplifying x + 2 = -3.535533906 Reorder the terms: 2 + x = -3.535533906 Solving 2 + x = -3.535533906 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 = -3.535533906 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.535533906 + -2 x = -3.535533906 + -2 Combine like terms: -3.535533906 + -2 = -5.535533906 x = -5.535533906 Simplifying x = -5.535533906Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.535533906, -5.535533906}Solution
x = {1.535533906, -5.535533906}
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