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Simplifying 11x2 + -168x + 63 = 0 Reorder the terms: 63 + -168x + 11x2 = 0 Solving 63 + -168x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 5.727272727 + -15.27272727x + x2 = 0 Move the constant term to the right: Add '-5.727272727' to each side of the equation. 5.727272727 + -15.27272727x + -5.727272727 + x2 = 0 + -5.727272727 Reorder the terms: 5.727272727 + -5.727272727 + -15.27272727x + x2 = 0 + -5.727272727 Combine like terms: 5.727272727 + -5.727272727 = 0.000000000 0.000000000 + -15.27272727x + x2 = 0 + -5.727272727 -15.27272727x + x2 = 0 + -5.727272727 Combine like terms: 0 + -5.727272727 = -5.727272727 -15.27272727x + x2 = -5.727272727 The x term is -15.27272727x. Take half its coefficient (-7.636363635). Square it (58.31404957) and add it to both sides. Add '58.31404957' to each side of the equation. -15.27272727x + 58.31404957 + x2 = -5.727272727 + 58.31404957 Reorder the terms: 58.31404957 + -15.27272727x + x2 = -5.727272727 + 58.31404957 Combine like terms: -5.727272727 + 58.31404957 = 52.586776843 58.31404957 + -15.27272727x + x2 = 52.586776843 Factor a perfect square on the left side: (x + -7.636363635)(x + -7.636363635) = 52.586776843 Calculate the square root of the right side: 7.251674072 Break this problem into two subproblems by setting (x + -7.636363635) equal to 7.251674072 and -7.251674072.Subproblem 1
x + -7.636363635 = 7.251674072 Simplifying x + -7.636363635 = 7.251674072 Reorder the terms: -7.636363635 + x = 7.251674072 Solving -7.636363635 + x = 7.251674072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.636363635' to each side of the equation. -7.636363635 + 7.636363635 + x = 7.251674072 + 7.636363635 Combine like terms: -7.636363635 + 7.636363635 = 0.000000000 0.000000000 + x = 7.251674072 + 7.636363635 x = 7.251674072 + 7.636363635 Combine like terms: 7.251674072 + 7.636363635 = 14.888037707 x = 14.888037707 Simplifying x = 14.888037707Subproblem 2
x + -7.636363635 = -7.251674072 Simplifying x + -7.636363635 = -7.251674072 Reorder the terms: -7.636363635 + x = -7.251674072 Solving -7.636363635 + x = -7.251674072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.636363635' to each side of the equation. -7.636363635 + 7.636363635 + x = -7.251674072 + 7.636363635 Combine like terms: -7.636363635 + 7.636363635 = 0.000000000 0.000000000 + x = -7.251674072 + 7.636363635 x = -7.251674072 + 7.636363635 Combine like terms: -7.251674072 + 7.636363635 = 0.384689563 x = 0.384689563 Simplifying x = 0.384689563Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.888037707, 0.384689563}
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