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Simplifying 7x2 + -27x + 8 = 0 Reorder the terms: 8 + -27x + 7x2 = 0 Solving 8 + -27x + 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'. 1.142857143 + -3.857142857x + x2 = 0 Move the constant term to the right: Add '-1.142857143' to each side of the equation. 1.142857143 + -3.857142857x + -1.142857143 + x2 = 0 + -1.142857143 Reorder the terms: 1.142857143 + -1.142857143 + -3.857142857x + x2 = 0 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + -3.857142857x + x2 = 0 + -1.142857143 -3.857142857x + x2 = 0 + -1.142857143 Combine like terms: 0 + -1.142857143 = -1.142857143 -3.857142857x + x2 = -1.142857143 The x term is -3.857142857x. Take half its coefficient (-1.928571429). Square it (3.719387757) and add it to both sides. Add '3.719387757' to each side of the equation. -3.857142857x + 3.719387757 + x2 = -1.142857143 + 3.719387757 Reorder the terms: 3.719387757 + -3.857142857x + x2 = -1.142857143 + 3.719387757 Combine like terms: -1.142857143 + 3.719387757 = 2.576530614 3.719387757 + -3.857142857x + x2 = 2.576530614 Factor a perfect square on the left side: (x + -1.928571429)(x + -1.928571429) = 2.576530614 Calculate the square root of the right side: 1.605157504 Break this problem into two subproblems by setting (x + -1.928571429) equal to 1.605157504 and -1.605157504.Subproblem 1
x + -1.928571429 = 1.605157504 Simplifying x + -1.928571429 = 1.605157504 Reorder the terms: -1.928571429 + x = 1.605157504 Solving -1.928571429 + x = 1.605157504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.928571429' to each side of the equation. -1.928571429 + 1.928571429 + x = 1.605157504 + 1.928571429 Combine like terms: -1.928571429 + 1.928571429 = 0.000000000 0.000000000 + x = 1.605157504 + 1.928571429 x = 1.605157504 + 1.928571429 Combine like terms: 1.605157504 + 1.928571429 = 3.533728933 x = 3.533728933 Simplifying x = 3.533728933Subproblem 2
x + -1.928571429 = -1.605157504 Simplifying x + -1.928571429 = -1.605157504 Reorder the terms: -1.928571429 + x = -1.605157504 Solving -1.928571429 + x = -1.605157504 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.928571429' to each side of the equation. -1.928571429 + 1.928571429 + x = -1.605157504 + 1.928571429 Combine like terms: -1.928571429 + 1.928571429 = 0.000000000 0.000000000 + x = -1.605157504 + 1.928571429 x = -1.605157504 + 1.928571429 Combine like terms: -1.605157504 + 1.928571429 = 0.323413925 x = 0.323413925 Simplifying x = 0.323413925Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.533728933, 0.323413925}
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