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Simplifying 22x2 + 34x + -100 = 0 Reorder the terms: -100 + 34x + 22x2 = 0 Solving -100 + 34x + 22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 17x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 17x + 11x2)' equal to zero and attempt to solve: Simplifying -50 + 17x + 11x2 = 0 Solving -50 + 17x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -4.545454545 + 1.545454545x + x2 = 0 Move the constant term to the right: Add '4.545454545' to each side of the equation. -4.545454545 + 1.545454545x + 4.545454545 + x2 = 0 + 4.545454545 Reorder the terms: -4.545454545 + 4.545454545 + 1.545454545x + x2 = 0 + 4.545454545 Combine like terms: -4.545454545 + 4.545454545 = 0.000000000 0.000000000 + 1.545454545x + x2 = 0 + 4.545454545 1.545454545x + x2 = 0 + 4.545454545 Combine like terms: 0 + 4.545454545 = 4.545454545 1.545454545x + x2 = 4.545454545 The x term is 1.545454545x. Take half its coefficient (0.7727272725). Square it (0.5971074377) and add it to both sides. Add '0.5971074377' to each side of the equation. 1.545454545x + 0.5971074377 + x2 = 4.545454545 + 0.5971074377 Reorder the terms: 0.5971074377 + 1.545454545x + x2 = 4.545454545 + 0.5971074377 Combine like terms: 4.545454545 + 0.5971074377 = 5.1425619827 0.5971074377 + 1.545454545x + x2 = 5.1425619827 Factor a perfect square on the left side: (x + 0.7727272725)(x + 0.7727272725) = 5.1425619827 Calculate the square root of the right side: 2.26772176 Break this problem into two subproblems by setting (x + 0.7727272725) equal to 2.26772176 and -2.26772176.Subproblem 1
x + 0.7727272725 = 2.26772176 Simplifying x + 0.7727272725 = 2.26772176 Reorder the terms: 0.7727272725 + x = 2.26772176 Solving 0.7727272725 + x = 2.26772176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7727272725' to each side of the equation. 0.7727272725 + -0.7727272725 + x = 2.26772176 + -0.7727272725 Combine like terms: 0.7727272725 + -0.7727272725 = 0.0000000000 0.0000000000 + x = 2.26772176 + -0.7727272725 x = 2.26772176 + -0.7727272725 Combine like terms: 2.26772176 + -0.7727272725 = 1.4949944875 x = 1.4949944875 Simplifying x = 1.4949944875Subproblem 2
x + 0.7727272725 = -2.26772176 Simplifying x + 0.7727272725 = -2.26772176 Reorder the terms: 0.7727272725 + x = -2.26772176 Solving 0.7727272725 + x = -2.26772176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7727272725' to each side of the equation. 0.7727272725 + -0.7727272725 + x = -2.26772176 + -0.7727272725 Combine like terms: 0.7727272725 + -0.7727272725 = 0.0000000000 0.0000000000 + x = -2.26772176 + -0.7727272725 x = -2.26772176 + -0.7727272725 Combine like terms: -2.26772176 + -0.7727272725 = -3.0404490325 x = -3.0404490325 Simplifying x = -3.0404490325Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4949944875, -3.0404490325}Solution
x = {1.4949944875, -3.0404490325}
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