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Simplifying 13x2 + -144x + 9 = 0 Reorder the terms: 9 + -144x + 13x2 = 0 Solving 9 + -144x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.6923076923 + -11.07692308x + x2 = 0 Move the constant term to the right: Add '-0.6923076923' to each side of the equation. 0.6923076923 + -11.07692308x + -0.6923076923 + x2 = 0 + -0.6923076923 Reorder the terms: 0.6923076923 + -0.6923076923 + -11.07692308x + x2 = 0 + -0.6923076923 Combine like terms: 0.6923076923 + -0.6923076923 = 0.0000000000 0.0000000000 + -11.07692308x + x2 = 0 + -0.6923076923 -11.07692308x + x2 = 0 + -0.6923076923 Combine like terms: 0 + -0.6923076923 = -0.6923076923 -11.07692308x + x2 = -0.6923076923 The x term is -11.07692308x. Take half its coefficient (-5.53846154). Square it (30.67455623) and add it to both sides. Add '30.67455623' to each side of the equation. -11.07692308x + 30.67455623 + x2 = -0.6923076923 + 30.67455623 Reorder the terms: 30.67455623 + -11.07692308x + x2 = -0.6923076923 + 30.67455623 Combine like terms: -0.6923076923 + 30.67455623 = 29.9822485377 30.67455623 + -11.07692308x + x2 = 29.9822485377 Factor a perfect square on the left side: (x + -5.53846154)(x + -5.53846154) = 29.9822485377 Calculate the square root of the right side: 5.475604856 Break this problem into two subproblems by setting (x + -5.53846154) equal to 5.475604856 and -5.475604856.Subproblem 1
x + -5.53846154 = 5.475604856 Simplifying x + -5.53846154 = 5.475604856 Reorder the terms: -5.53846154 + x = 5.475604856 Solving -5.53846154 + x = 5.475604856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.53846154' to each side of the equation. -5.53846154 + 5.53846154 + x = 5.475604856 + 5.53846154 Combine like terms: -5.53846154 + 5.53846154 = 0.00000000 0.00000000 + x = 5.475604856 + 5.53846154 x = 5.475604856 + 5.53846154 Combine like terms: 5.475604856 + 5.53846154 = 11.014066396 x = 11.014066396 Simplifying x = 11.014066396Subproblem 2
x + -5.53846154 = -5.475604856 Simplifying x + -5.53846154 = -5.475604856 Reorder the terms: -5.53846154 + x = -5.475604856 Solving -5.53846154 + x = -5.475604856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.53846154' to each side of the equation. -5.53846154 + 5.53846154 + x = -5.475604856 + 5.53846154 Combine like terms: -5.53846154 + 5.53846154 = 0.00000000 0.00000000 + x = -5.475604856 + 5.53846154 x = -5.475604856 + 5.53846154 Combine like terms: -5.475604856 + 5.53846154 = 0.062856684 x = 0.062856684 Simplifying x = 0.062856684Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.014066396, 0.062856684}
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