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Simplifying 7x2 + -54x + 81 = 0 Reorder the terms: 81 + -54x + 7x2 = 0 Solving 81 + -54x + 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'. 11.57142857 + -7.714285714x + x2 = 0 Move the constant term to the right: Add '-11.57142857' to each side of the equation. 11.57142857 + -7.714285714x + -11.57142857 + x2 = 0 + -11.57142857 Reorder the terms: 11.57142857 + -11.57142857 + -7.714285714x + x2 = 0 + -11.57142857 Combine like terms: 11.57142857 + -11.57142857 = 0.00000000 0.00000000 + -7.714285714x + x2 = 0 + -11.57142857 -7.714285714x + x2 = 0 + -11.57142857 Combine like terms: 0 + -11.57142857 = -11.57142857 -7.714285714x + x2 = -11.57142857 The x term is -7.714285714x. Take half its coefficient (-3.857142857). Square it (14.87755102) and add it to both sides. Add '14.87755102' to each side of the equation. -7.714285714x + 14.87755102 + x2 = -11.57142857 + 14.87755102 Reorder the terms: 14.87755102 + -7.714285714x + x2 = -11.57142857 + 14.87755102 Combine like terms: -11.57142857 + 14.87755102 = 3.30612245 14.87755102 + -7.714285714x + x2 = 3.30612245 Factor a perfect square on the left side: (x + -3.857142857)(x + -3.857142857) = 3.30612245 Calculate the square root of the right side: 1.81827458 Break this problem into two subproblems by setting (x + -3.857142857) equal to 1.81827458 and -1.81827458.Subproblem 1
x + -3.857142857 = 1.81827458 Simplifying x + -3.857142857 = 1.81827458 Reorder the terms: -3.857142857 + x = 1.81827458 Solving -3.857142857 + x = 1.81827458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.857142857' to each side of the equation. -3.857142857 + 3.857142857 + x = 1.81827458 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + x = 1.81827458 + 3.857142857 x = 1.81827458 + 3.857142857 Combine like terms: 1.81827458 + 3.857142857 = 5.675417437 x = 5.675417437 Simplifying x = 5.675417437Subproblem 2
x + -3.857142857 = -1.81827458 Simplifying x + -3.857142857 = -1.81827458 Reorder the terms: -3.857142857 + x = -1.81827458 Solving -3.857142857 + x = -1.81827458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.857142857' to each side of the equation. -3.857142857 + 3.857142857 + x = -1.81827458 + 3.857142857 Combine like terms: -3.857142857 + 3.857142857 = 0.000000000 0.000000000 + x = -1.81827458 + 3.857142857 x = -1.81827458 + 3.857142857 Combine like terms: -1.81827458 + 3.857142857 = 2.038868277 x = 2.038868277 Simplifying x = 2.038868277Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.675417437, 2.038868277}
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