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Simplifying 4x2 + -8x + -122 = 0 Reorder the terms: -122 + -8x + 4x2 = 0 Solving -122 + -8x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-61 + -4x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-61 + -4x + 2x2)' equal to zero and attempt to solve: Simplifying -61 + -4x + 2x2 = 0 Solving -61 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -30.5 + -2x + x2 = 0 Move the constant term to the right: Add '30.5' to each side of the equation. -30.5 + -2x + 30.5 + x2 = 0 + 30.5 Reorder the terms: -30.5 + 30.5 + -2x + x2 = 0 + 30.5 Combine like terms: -30.5 + 30.5 = 0.0 0.0 + -2x + x2 = 0 + 30.5 -2x + x2 = 0 + 30.5 Combine like terms: 0 + 30.5 = 30.5 -2x + x2 = 30.5 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 = 30.5 + 1 Reorder the terms: 1 + -2x + x2 = 30.5 + 1 Combine like terms: 30.5 + 1 = 31.5 1 + -2x + x2 = 31.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 31.5 Calculate the square root of the right side: 5.61248608 Break this problem into two subproblems by setting (x + -1) equal to 5.61248608 and -5.61248608.Subproblem 1
x + -1 = 5.61248608 Simplifying x + -1 = 5.61248608 Reorder the terms: -1 + x = 5.61248608 Solving -1 + x = 5.61248608 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 = 5.61248608 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.61248608 + 1 x = 5.61248608 + 1 Combine like terms: 5.61248608 + 1 = 6.61248608 x = 6.61248608 Simplifying x = 6.61248608Subproblem 2
x + -1 = -5.61248608 Simplifying x + -1 = -5.61248608 Reorder the terms: -1 + x = -5.61248608 Solving -1 + x = -5.61248608 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 = -5.61248608 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.61248608 + 1 x = -5.61248608 + 1 Combine like terms: -5.61248608 + 1 = -4.61248608 x = -4.61248608 Simplifying x = -4.61248608Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.61248608, -4.61248608}Solution
x = {6.61248608, -4.61248608}
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