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Simplifying 5x2 + -22x + -124 = 0 Reorder the terms: -124 + -22x + 5x2 = 0 Solving -124 + -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'. -24.8 + -4.4x + x2 = 0 Move the constant term to the right: Add '24.8' to each side of the equation. -24.8 + -4.4x + 24.8 + x2 = 0 + 24.8 Reorder the terms: -24.8 + 24.8 + -4.4x + x2 = 0 + 24.8 Combine like terms: -24.8 + 24.8 = 0.0 0.0 + -4.4x + x2 = 0 + 24.8 -4.4x + x2 = 0 + 24.8 Combine like terms: 0 + 24.8 = 24.8 -4.4x + x2 = 24.8 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 = 24.8 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = 24.8 + 4.84 Combine like terms: 24.8 + 4.84 = 29.64 4.84 + -4.4x + x2 = 29.64 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 29.64 Calculate the square root of the right side: 5.444263036 Break this problem into two subproblems by setting (x + -2.2) equal to 5.444263036 and -5.444263036.Subproblem 1
x + -2.2 = 5.444263036 Simplifying x + -2.2 = 5.444263036 Reorder the terms: -2.2 + x = 5.444263036 Solving -2.2 + x = 5.444263036 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 = 5.444263036 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 5.444263036 + 2.2 x = 5.444263036 + 2.2 Combine like terms: 5.444263036 + 2.2 = 7.644263036 x = 7.644263036 Simplifying x = 7.644263036Subproblem 2
x + -2.2 = -5.444263036 Simplifying x + -2.2 = -5.444263036 Reorder the terms: -2.2 + x = -5.444263036 Solving -2.2 + x = -5.444263036 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 = -5.444263036 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -5.444263036 + 2.2 x = -5.444263036 + 2.2 Combine like terms: -5.444263036 + 2.2 = -3.244263036 x = -3.244263036 Simplifying x = -3.244263036Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.644263036, -3.244263036}
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