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Simplifying 13x2 + -24x + 4 = 0 Reorder the terms: 4 + -24x + 13x2 = 0 Solving 4 + -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'. 0.3076923077 + -1.846153846x + x2 = 0 Move the constant term to the right: Add '-0.3076923077' to each side of the equation. 0.3076923077 + -1.846153846x + -0.3076923077 + x2 = 0 + -0.3076923077 Reorder the terms: 0.3076923077 + -0.3076923077 + -1.846153846x + x2 = 0 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + -1.846153846x + x2 = 0 + -0.3076923077 -1.846153846x + x2 = 0 + -0.3076923077 Combine like terms: 0 + -0.3076923077 = -0.3076923077 -1.846153846x + x2 = -0.3076923077 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 = -0.3076923077 + 0.8520710058 Reorder the terms: 0.8520710058 + -1.846153846x + x2 = -0.3076923077 + 0.8520710058 Combine like terms: -0.3076923077 + 0.8520710058 = 0.5443786981 0.8520710058 + -1.846153846x + x2 = 0.5443786981 Factor a perfect square on the left side: (x + -0.923076923)(x + -0.923076923) = 0.5443786981 Calculate the square root of the right side: 0.737820234 Break this problem into two subproblems by setting (x + -0.923076923) equal to 0.737820234 and -0.737820234.Subproblem 1
x + -0.923076923 = 0.737820234 Simplifying x + -0.923076923 = 0.737820234 Reorder the terms: -0.923076923 + x = 0.737820234 Solving -0.923076923 + x = 0.737820234 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 = 0.737820234 + 0.923076923 Combine like terms: -0.923076923 + 0.923076923 = 0.000000000 0.000000000 + x = 0.737820234 + 0.923076923 x = 0.737820234 + 0.923076923 Combine like terms: 0.737820234 + 0.923076923 = 1.660897157 x = 1.660897157 Simplifying x = 1.660897157Subproblem 2
x + -0.923076923 = -0.737820234 Simplifying x + -0.923076923 = -0.737820234 Reorder the terms: -0.923076923 + x = -0.737820234 Solving -0.923076923 + x = -0.737820234 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 = -0.737820234 + 0.923076923 Combine like terms: -0.923076923 + 0.923076923 = 0.000000000 0.000000000 + x = -0.737820234 + 0.923076923 x = -0.737820234 + 0.923076923 Combine like terms: -0.737820234 + 0.923076923 = 0.185256689 x = 0.185256689 Simplifying x = 0.185256689Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.660897157, 0.185256689}
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