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Simplifying 4x2 + 22x + -4 = 0 Reorder the terms: -4 + 22x + 4x2 = 0 Solving -4 + 22x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 11x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 11x + 2x2)' equal to zero and attempt to solve: Simplifying -2 + 11x + 2x2 = 0 Solving -2 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + 5.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 5.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 5.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5.5x + x2 = 0 + 1 5.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 5.5x + x2 = 1 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 1 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 1 + 7.5625 Combine like terms: 1 + 7.5625 = 8.5625 7.5625 + 5.5x + x2 = 8.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (x + 2.75) equal to 2.926174978 and -2.926174978.Subproblem 1
x + 2.75 = 2.926174978 Simplifying x + 2.75 = 2.926174978 Reorder the terms: 2.75 + x = 2.926174978 Solving 2.75 + x = 2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 2.926174978 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 2.926174978 + -2.75 x = 2.926174978 + -2.75 Combine like terms: 2.926174978 + -2.75 = 0.176174978 x = 0.176174978 Simplifying x = 0.176174978Subproblem 2
x + 2.75 = -2.926174978 Simplifying x + 2.75 = -2.926174978 Reorder the terms: 2.75 + x = -2.926174978 Solving 2.75 + x = -2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -2.926174978 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -2.926174978 + -2.75 x = -2.926174978 + -2.75 Combine like terms: -2.926174978 + -2.75 = -5.676174978 x = -5.676174978 Simplifying x = -5.676174978Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.176174978, -5.676174978}Solution
x = {0.176174978, -5.676174978}
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