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Simplifying 4x2 + 8x + -174 = 0 Reorder the terms: -174 + 8x + 4x2 = 0 Solving -174 + 8x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-87 + 4x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-87 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying -87 + 4x + 2x2 = 0 Solving -87 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -43.5 + 2x + x2 = 0 Move the constant term to the right: Add '43.5' to each side of the equation. -43.5 + 2x + 43.5 + x2 = 0 + 43.5 Reorder the terms: -43.5 + 43.5 + 2x + x2 = 0 + 43.5 Combine like terms: -43.5 + 43.5 = 0.0 0.0 + 2x + x2 = 0 + 43.5 2x + x2 = 0 + 43.5 Combine like terms: 0 + 43.5 = 43.5 2x + x2 = 43.5 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 = 43.5 + 1 Reorder the terms: 1 + 2x + x2 = 43.5 + 1 Combine like terms: 43.5 + 1 = 44.5 1 + 2x + x2 = 44.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 44.5 Calculate the square root of the right side: 6.670832032 Break this problem into two subproblems by setting (x + 1) equal to 6.670832032 and -6.670832032.Subproblem 1
x + 1 = 6.670832032 Simplifying x + 1 = 6.670832032 Reorder the terms: 1 + x = 6.670832032 Solving 1 + x = 6.670832032 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 = 6.670832032 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.670832032 + -1 x = 6.670832032 + -1 Combine like terms: 6.670832032 + -1 = 5.670832032 x = 5.670832032 Simplifying x = 5.670832032Subproblem 2
x + 1 = -6.670832032 Simplifying x + 1 = -6.670832032 Reorder the terms: 1 + x = -6.670832032 Solving 1 + x = -6.670832032 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 = -6.670832032 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.670832032 + -1 x = -6.670832032 + -1 Combine like terms: -6.670832032 + -1 = -7.670832032 x = -7.670832032 Simplifying x = -7.670832032Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.670832032, -7.670832032}Solution
x = {5.670832032, -7.670832032}
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