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Simplifying 19x2 + 102x + -118 = 0 Reorder the terms: -118 + 102x + 19x2 = 0 Solving -118 + 102x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -6.210526316 + 5.368421053x + x2 = 0 Move the constant term to the right: Add '6.210526316' to each side of the equation. -6.210526316 + 5.368421053x + 6.210526316 + x2 = 0 + 6.210526316 Reorder the terms: -6.210526316 + 6.210526316 + 5.368421053x + x2 = 0 + 6.210526316 Combine like terms: -6.210526316 + 6.210526316 = 0.000000000 0.000000000 + 5.368421053x + x2 = 0 + 6.210526316 5.368421053x + x2 = 0 + 6.210526316 Combine like terms: 0 + 6.210526316 = 6.210526316 5.368421053x + x2 = 6.210526316 The x term is 5.368421053x. Take half its coefficient (2.684210527). Square it (7.204986153) and add it to both sides. Add '7.204986153' to each side of the equation. 5.368421053x + 7.204986153 + x2 = 6.210526316 + 7.204986153 Reorder the terms: 7.204986153 + 5.368421053x + x2 = 6.210526316 + 7.204986153 Combine like terms: 6.210526316 + 7.204986153 = 13.415512469 7.204986153 + 5.368421053x + x2 = 13.415512469 Factor a perfect square on the left side: (x + 2.684210527)(x + 2.684210527) = 13.415512469 Calculate the square root of the right side: 3.662719272 Break this problem into two subproblems by setting (x + 2.684210527) equal to 3.662719272 and -3.662719272.Subproblem 1
x + 2.684210527 = 3.662719272 Simplifying x + 2.684210527 = 3.662719272 Reorder the terms: 2.684210527 + x = 3.662719272 Solving 2.684210527 + x = 3.662719272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.684210527' to each side of the equation. 2.684210527 + -2.684210527 + x = 3.662719272 + -2.684210527 Combine like terms: 2.684210527 + -2.684210527 = 0.000000000 0.000000000 + x = 3.662719272 + -2.684210527 x = 3.662719272 + -2.684210527 Combine like terms: 3.662719272 + -2.684210527 = 0.978508745 x = 0.978508745 Simplifying x = 0.978508745Subproblem 2
x + 2.684210527 = -3.662719272 Simplifying x + 2.684210527 = -3.662719272 Reorder the terms: 2.684210527 + x = -3.662719272 Solving 2.684210527 + x = -3.662719272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.684210527' to each side of the equation. 2.684210527 + -2.684210527 + x = -3.662719272 + -2.684210527 Combine like terms: 2.684210527 + -2.684210527 = 0.000000000 0.000000000 + x = -3.662719272 + -2.684210527 x = -3.662719272 + -2.684210527 Combine like terms: -3.662719272 + -2.684210527 = -6.346929799 x = -6.346929799 Simplifying x = -6.346929799Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.978508745, -6.346929799}
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