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Simplifying 5x2 + -22x + -13 = 0 Reorder the terms: -13 + -22x + 5x2 = 0 Solving -13 + -22x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + -4.4x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -4.4x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -4.4x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -4.4x + x2 = 0 + 2.6 -4.4x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -4.4x + x2 = 2.6 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = 2.6 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = 2.6 + 4.84 Combine like terms: 2.6 + 4.84 = 7.44 4.84 + -4.4x + x2 = 7.44 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 7.44 Calculate the square root of the right side: 2.727636339 Break this problem into two subproblems by setting (x + -2.2) equal to 2.727636339 and -2.727636339.Subproblem 1
x + -2.2 = 2.727636339 Simplifying x + -2.2 = 2.727636339 Reorder the terms: -2.2 + x = 2.727636339 Solving -2.2 + x = 2.727636339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 2.727636339 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 2.727636339 + 2.2 x = 2.727636339 + 2.2 Combine like terms: 2.727636339 + 2.2 = 4.927636339 x = 4.927636339 Simplifying x = 4.927636339Subproblem 2
x + -2.2 = -2.727636339 Simplifying x + -2.2 = -2.727636339 Reorder the terms: -2.2 + x = -2.727636339 Solving -2.2 + x = -2.727636339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -2.727636339 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -2.727636339 + 2.2 x = -2.727636339 + 2.2 Combine like terms: -2.727636339 + 2.2 = -0.527636339 x = -0.527636339 Simplifying x = -0.527636339Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.927636339, -0.527636339}
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