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Simplifying -1x2 + -22x + -47 = 0 Reorder the terms: -47 + -22x + -1x2 = 0 Solving -47 + -22x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(47 + 22x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(47 + 22x + x2)' equal to zero and attempt to solve: Simplifying 47 + 22x + x2 = 0 Solving 47 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + 22x + -47 + x2 = 0 + -47 Reorder the terms: 47 + -47 + 22x + x2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + 22x + x2 = 0 + -47 22x + x2 = 0 + -47 Combine like terms: 0 + -47 = -47 22x + x2 = -47 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = -47 + 121 Reorder the terms: 121 + 22x + x2 = -47 + 121 Combine like terms: -47 + 121 = 74 121 + 22x + x2 = 74 Factor a perfect square on the left side: (x + 11)(x + 11) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (x + 11) equal to 8.602325267 and -8.602325267.Subproblem 1
x + 11 = 8.602325267 Simplifying x + 11 = 8.602325267 Reorder the terms: 11 + x = 8.602325267 Solving 11 + x = 8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 8.602325267 + -11 Combine like terms: 11 + -11 = 0 0 + x = 8.602325267 + -11 x = 8.602325267 + -11 Combine like terms: 8.602325267 + -11 = -2.397674733 x = -2.397674733 Simplifying x = -2.397674733Subproblem 2
x + 11 = -8.602325267 Simplifying x + 11 = -8.602325267 Reorder the terms: 11 + x = -8.602325267 Solving 11 + x = -8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -8.602325267 + -11 Combine like terms: 11 + -11 = 0 0 + x = -8.602325267 + -11 x = -8.602325267 + -11 Combine like terms: -8.602325267 + -11 = -19.602325267 x = -19.602325267 Simplifying x = -19.602325267Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.397674733, -19.602325267}Solution
x = {-2.397674733, -19.602325267}
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