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Simplifying 7x2 + -55x + 72 = 0 Reorder the terms: 72 + -55x + 7x2 = 0 Solving 72 + -55x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 10.28571429 + -7.857142857x + x2 = 0 Move the constant term to the right: Add '-10.28571429' to each side of the equation. 10.28571429 + -7.857142857x + -10.28571429 + x2 = 0 + -10.28571429 Reorder the terms: 10.28571429 + -10.28571429 + -7.857142857x + x2 = 0 + -10.28571429 Combine like terms: 10.28571429 + -10.28571429 = 0.00000000 0.00000000 + -7.857142857x + x2 = 0 + -10.28571429 -7.857142857x + x2 = 0 + -10.28571429 Combine like terms: 0 + -10.28571429 = -10.28571429 -7.857142857x + x2 = -10.28571429 The x term is -7.857142857x. Take half its coefficient (-3.928571429). Square it (15.43367347) and add it to both sides. Add '15.43367347' to each side of the equation. -7.857142857x + 15.43367347 + x2 = -10.28571429 + 15.43367347 Reorder the terms: 15.43367347 + -7.857142857x + x2 = -10.28571429 + 15.43367347 Combine like terms: -10.28571429 + 15.43367347 = 5.14795918 15.43367347 + -7.857142857x + x2 = 5.14795918 Factor a perfect square on the left side: (x + -3.928571429)(x + -3.928571429) = 5.14795918 Calculate the square root of the right side: 2.268911453 Break this problem into two subproblems by setting (x + -3.928571429) equal to 2.268911453 and -2.268911453.Subproblem 1
x + -3.928571429 = 2.268911453 Simplifying x + -3.928571429 = 2.268911453 Reorder the terms: -3.928571429 + x = 2.268911453 Solving -3.928571429 + x = 2.268911453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.928571429' to each side of the equation. -3.928571429 + 3.928571429 + x = 2.268911453 + 3.928571429 Combine like terms: -3.928571429 + 3.928571429 = 0.000000000 0.000000000 + x = 2.268911453 + 3.928571429 x = 2.268911453 + 3.928571429 Combine like terms: 2.268911453 + 3.928571429 = 6.197482882 x = 6.197482882 Simplifying x = 6.197482882Subproblem 2
x + -3.928571429 = -2.268911453 Simplifying x + -3.928571429 = -2.268911453 Reorder the terms: -3.928571429 + x = -2.268911453 Solving -3.928571429 + x = -2.268911453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.928571429' to each side of the equation. -3.928571429 + 3.928571429 + x = -2.268911453 + 3.928571429 Combine like terms: -3.928571429 + 3.928571429 = 0.000000000 0.000000000 + x = -2.268911453 + 3.928571429 x = -2.268911453 + 3.928571429 Combine like terms: -2.268911453 + 3.928571429 = 1.659659976 x = 1.659659976 Simplifying x = 1.659659976Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.197482882, 1.659659976}
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