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Simplifying 13X + 13X2 = 9 Solving 13X + 13X2 = 9 Solving for variable 'X'. Reorder the terms: -9 + 13X + 13X2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 13X + 13X2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.6923076923 + X + X2 = 0 Move the constant term to the right: Add '0.6923076923' to each side of the equation. -0.6923076923 + X + 0.6923076923 + X2 = 0 + 0.6923076923 Reorder the terms: -0.6923076923 + 0.6923076923 + X + X2 = 0 + 0.6923076923 Combine like terms: -0.6923076923 + 0.6923076923 = 0.0000000000 0.0000000000 + X + X2 = 0 + 0.6923076923 X + X2 = 0 + 0.6923076923 Combine like terms: 0 + 0.6923076923 = 0.6923076923 X + X2 = 0.6923076923 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + X2 = 0.6923076923 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + X2 = 0.6923076923 + 0.25 Combine like terms: 0.6923076923 + 0.25 = 0.9423076923 1.25 + X2 = 0.9423076923 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 0.9423076923 Calculate the square root of the right side: 0.970725343 Break this problem into two subproblems by setting (X + 0.5) equal to 0.970725343 and -0.970725343.Subproblem 1
X + 0.5 = 0.970725343 Simplifying X + 0.5 = 0.970725343 Reorder the terms: 0.5 + X = 0.970725343 Solving 0.5 + X = 0.970725343 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 0.970725343 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 0.970725343 + -0.5 X = 0.970725343 + -0.5 Combine like terms: 0.970725343 + -0.5 = 0.470725343 X = 0.470725343 Simplifying X = 0.470725343Subproblem 2
X + 0.5 = -0.970725343 Simplifying X + 0.5 = -0.970725343 Reorder the terms: 0.5 + X = -0.970725343 Solving 0.5 + X = -0.970725343 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -0.970725343 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -0.970725343 + -0.5 X = -0.970725343 + -0.5 Combine like terms: -0.970725343 + -0.5 = -1.470725343 X = -1.470725343 Simplifying X = -1.470725343Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.470725343, -1.470725343}
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