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Simplifying 11x2 + 168x + -784 = 0 Reorder the terms: -784 + 168x + 11x2 = 0 Solving -784 + 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'. -71.27272727 + 15.27272727x + x2 = 0 Move the constant term to the right: Add '71.27272727' to each side of the equation. -71.27272727 + 15.27272727x + 71.27272727 + x2 = 0 + 71.27272727 Reorder the terms: -71.27272727 + 71.27272727 + 15.27272727x + x2 = 0 + 71.27272727 Combine like terms: -71.27272727 + 71.27272727 = 0.00000000 0.00000000 + 15.27272727x + x2 = 0 + 71.27272727 15.27272727x + x2 = 0 + 71.27272727 Combine like terms: 0 + 71.27272727 = 71.27272727 15.27272727x + x2 = 71.27272727 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 = 71.27272727 + 58.31404957 Reorder the terms: 58.31404957 + 15.27272727x + x2 = 71.27272727 + 58.31404957 Combine like terms: 71.27272727 + 58.31404957 = 129.58677684 58.31404957 + 15.27272727x + x2 = 129.58677684 Factor a perfect square on the left side: (x + 7.636363635)(x + 7.636363635) = 129.58677684 Calculate the square root of the right side: 11.383618794 Break this problem into two subproblems by setting (x + 7.636363635) equal to 11.383618794 and -11.383618794.Subproblem 1
x + 7.636363635 = 11.383618794 Simplifying x + 7.636363635 = 11.383618794 Reorder the terms: 7.636363635 + x = 11.383618794 Solving 7.636363635 + x = 11.383618794 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 = 11.383618794 + -7.636363635 Combine like terms: 7.636363635 + -7.636363635 = 0.000000000 0.000000000 + x = 11.383618794 + -7.636363635 x = 11.383618794 + -7.636363635 Combine like terms: 11.383618794 + -7.636363635 = 3.747255159 x = 3.747255159 Simplifying x = 3.747255159Subproblem 2
x + 7.636363635 = -11.383618794 Simplifying x + 7.636363635 = -11.383618794 Reorder the terms: 7.636363635 + x = -11.383618794 Solving 7.636363635 + x = -11.383618794 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 = -11.383618794 + -7.636363635 Combine like terms: 7.636363635 + -7.636363635 = 0.000000000 0.000000000 + x = -11.383618794 + -7.636363635 x = -11.383618794 + -7.636363635 Combine like terms: -11.383618794 + -7.636363635 = -19.019982429 x = -19.019982429 Simplifying x = -19.019982429Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.747255159, -19.019982429}
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