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Simplifying 13x2 + -24x + -288 = 0 Reorder the terms: -288 + -24x + 13x2 = 0 Solving -288 + -24x + 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'. -22.15384615 + -1.846153846x + x2 = 0 Move the constant term to the right: Add '22.15384615' to each side of the equation. -22.15384615 + -1.846153846x + 22.15384615 + x2 = 0 + 22.15384615 Reorder the terms: -22.15384615 + 22.15384615 + -1.846153846x + x2 = 0 + 22.15384615 Combine like terms: -22.15384615 + 22.15384615 = 0.00000000 0.00000000 + -1.846153846x + x2 = 0 + 22.15384615 -1.846153846x + x2 = 0 + 22.15384615 Combine like terms: 0 + 22.15384615 = 22.15384615 -1.846153846x + x2 = 22.15384615 The x term is -1.846153846x. Take half its coefficient (-0.923076923). Square it (0.8520710058) and add it to both sides. Add '0.8520710058' to each side of the equation. -1.846153846x + 0.8520710058 + x2 = 22.15384615 + 0.8520710058 Reorder the terms: 0.8520710058 + -1.846153846x + x2 = 22.15384615 + 0.8520710058 Combine like terms: 22.15384615 + 0.8520710058 = 23.0059171558 0.8520710058 + -1.846153846x + x2 = 23.0059171558 Factor a perfect square on the left side: (x + -0.923076923)(x + -0.923076923) = 23.0059171558 Calculate the square root of the right side: 4.79644839 Break this problem into two subproblems by setting (x + -0.923076923) equal to 4.79644839 and -4.79644839.Subproblem 1
x + -0.923076923 = 4.79644839 Simplifying x + -0.923076923 = 4.79644839 Reorder the terms: -0.923076923 + x = 4.79644839 Solving -0.923076923 + x = 4.79644839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.923076923' to each side of the equation. -0.923076923 + 0.923076923 + x = 4.79644839 + 0.923076923 Combine like terms: -0.923076923 + 0.923076923 = 0.000000000 0.000000000 + x = 4.79644839 + 0.923076923 x = 4.79644839 + 0.923076923 Combine like terms: 4.79644839 + 0.923076923 = 5.719525313 x = 5.719525313 Simplifying x = 5.719525313Subproblem 2
x + -0.923076923 = -4.79644839 Simplifying x + -0.923076923 = -4.79644839 Reorder the terms: -0.923076923 + x = -4.79644839 Solving -0.923076923 + x = -4.79644839 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.923076923' to each side of the equation. -0.923076923 + 0.923076923 + x = -4.79644839 + 0.923076923 Combine like terms: -0.923076923 + 0.923076923 = 0.000000000 0.000000000 + x = -4.79644839 + 0.923076923 x = -4.79644839 + 0.923076923 Combine like terms: -4.79644839 + 0.923076923 = -3.873371467 x = -3.873371467 Simplifying x = -3.873371467Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.719525313, -3.873371467}
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