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Simplifying 5x2 + -52x + -13 = 0 Reorder the terms: -13 + -52x + 5x2 = 0 Solving -13 + -52x + 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 + -10.4x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + -10.4x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + -10.4x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + -10.4x + x2 = 0 + 2.6 -10.4x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 -10.4x + x2 = 2.6 The x term is -10.4x. Take half its coefficient (-5.2). Square it (27.04) and add it to both sides. Add '27.04' to each side of the equation. -10.4x + 27.04 + x2 = 2.6 + 27.04 Reorder the terms: 27.04 + -10.4x + x2 = 2.6 + 27.04 Combine like terms: 2.6 + 27.04 = 29.64 27.04 + -10.4x + x2 = 29.64 Factor a perfect square on the left side: (x + -5.2)(x + -5.2) = 29.64 Calculate the square root of the right side: 5.444263036 Break this problem into two subproblems by setting (x + -5.2) equal to 5.444263036 and -5.444263036.Subproblem 1
x + -5.2 = 5.444263036 Simplifying x + -5.2 = 5.444263036 Reorder the terms: -5.2 + x = 5.444263036 Solving -5.2 + x = 5.444263036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.2' to each side of the equation. -5.2 + 5.2 + x = 5.444263036 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + x = 5.444263036 + 5.2 x = 5.444263036 + 5.2 Combine like terms: 5.444263036 + 5.2 = 10.644263036 x = 10.644263036 Simplifying x = 10.644263036Subproblem 2
x + -5.2 = -5.444263036 Simplifying x + -5.2 = -5.444263036 Reorder the terms: -5.2 + x = -5.444263036 Solving -5.2 + x = -5.444263036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.2' to each side of the equation. -5.2 + 5.2 + x = -5.444263036 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + x = -5.444263036 + 5.2 x = -5.444263036 + 5.2 Combine like terms: -5.444263036 + 5.2 = -0.244263036 x = -0.244263036 Simplifying x = -0.244263036Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.644263036, -0.244263036}
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