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Simplifying 7x2 + -55x + 28 = 0 Reorder the terms: 28 + -55x + 7x2 = 0 Solving 28 + -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'. 4 + -7.857142857x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -7.857142857x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -7.857142857x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7.857142857x + x2 = 0 + -4 -7.857142857x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -7.857142857x + x2 = -4 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 = -4 + 15.43367347 Reorder the terms: 15.43367347 + -7.857142857x + x2 = -4 + 15.43367347 Combine like terms: -4 + 15.43367347 = 11.43367347 15.43367347 + -7.857142857x + x2 = 11.43367347 Factor a perfect square on the left side: (x + -3.928571429)(x + -3.928571429) = 11.43367347 Calculate the square root of the right side: 3.381371537 Break this problem into two subproblems by setting (x + -3.928571429) equal to 3.381371537 and -3.381371537.Subproblem 1
x + -3.928571429 = 3.381371537 Simplifying x + -3.928571429 = 3.381371537 Reorder the terms: -3.928571429 + x = 3.381371537 Solving -3.928571429 + x = 3.381371537 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 = 3.381371537 + 3.928571429 Combine like terms: -3.928571429 + 3.928571429 = 0.000000000 0.000000000 + x = 3.381371537 + 3.928571429 x = 3.381371537 + 3.928571429 Combine like terms: 3.381371537 + 3.928571429 = 7.309942966 x = 7.309942966 Simplifying x = 7.309942966Subproblem 2
x + -3.928571429 = -3.381371537 Simplifying x + -3.928571429 = -3.381371537 Reorder the terms: -3.928571429 + x = -3.381371537 Solving -3.928571429 + x = -3.381371537 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 = -3.381371537 + 3.928571429 Combine like terms: -3.928571429 + 3.928571429 = 0.000000000 0.000000000 + x = -3.381371537 + 3.928571429 x = -3.381371537 + 3.928571429 Combine like terms: -3.381371537 + 3.928571429 = 0.547199892 x = 0.547199892 Simplifying x = 0.547199892Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.309942966, 0.547199892}
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