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Simplifying 7X(X + -2) + 13(X + -3) = -3 Reorder the terms: 7X(-2 + X) + 13(X + -3) = -3 (-2 * 7X + X * 7X) + 13(X + -3) = -3 (-14X + 7X2) + 13(X + -3) = -3 Reorder the terms: -14X + 7X2 + 13(-3 + X) = -3 -14X + 7X2 + (-3 * 13 + X * 13) = -3 -14X + 7X2 + (-39 + 13X) = -3 Reorder the terms: -39 + -14X + 13X + 7X2 = -3 Combine like terms: -14X + 13X = -1X -39 + -1X + 7X2 = -3 Solving -39 + -1X + 7X2 = -3 Solving for variable 'X'. Reorder the terms: -39 + 3 + -1X + 7X2 = -3 + 3 Combine like terms: -39 + 3 = -36 -36 + -1X + 7X2 = -3 + 3 Combine like terms: -3 + 3 = 0 -36 + -1X + 7X2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.142857143 + -0.1428571429X + X2 = 0 Move the constant term to the right: Add '5.142857143' to each side of the equation. -5.142857143 + -0.1428571429X + 5.142857143 + X2 = 0 + 5.142857143 Reorder the terms: -5.142857143 + 5.142857143 + -0.1428571429X + X2 = 0 + 5.142857143 Combine like terms: -5.142857143 + 5.142857143 = 0.000000000 0.000000000 + -0.1428571429X + X2 = 0 + 5.142857143 -0.1428571429X + X2 = 0 + 5.142857143 Combine like terms: 0 + 5.142857143 = 5.142857143 -0.1428571429X + X2 = 5.142857143 The X term is -0.1428571429X. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429X + 0.005102040819 + X2 = 5.142857143 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429X + X2 = 5.142857143 + 0.005102040819 Combine like terms: 5.142857143 + 0.005102040819 = 5.147959183819 0.005102040819 + -0.1428571429X + X2 = 5.147959183819 Factor a perfect square on the left side: (X + -0.07142857145)(X + -0.07142857145) = 5.147959183819 Calculate the square root of the right side: 2.268911453 Break this problem into two subproblems by setting (X + -0.07142857145) equal to 2.268911453 and -2.268911453.Subproblem 1
X + -0.07142857145 = 2.268911453 Simplifying X + -0.07142857145 = 2.268911453 Reorder the terms: -0.07142857145 + X = 2.268911453 Solving -0.07142857145 + X = 2.268911453 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + X = 2.268911453 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + X = 2.268911453 + 0.07142857145 X = 2.268911453 + 0.07142857145 Combine like terms: 2.268911453 + 0.07142857145 = 2.34034002445 X = 2.34034002445 Simplifying X = 2.34034002445Subproblem 2
X + -0.07142857145 = -2.268911453 Simplifying X + -0.07142857145 = -2.268911453 Reorder the terms: -0.07142857145 + X = -2.268911453 Solving -0.07142857145 + X = -2.268911453 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + X = -2.268911453 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + X = -2.268911453 + 0.07142857145 X = -2.268911453 + 0.07142857145 Combine like terms: -2.268911453 + 0.07142857145 = -2.19748288155 X = -2.19748288155 Simplifying X = -2.19748288155Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.34034002445, -2.19748288155}
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