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Simplifying 19x2 + -209 = 17 * 6x + -53 Reorder the terms: -209 + 19x2 = 17 * 6x + -53 Multiply 17 * 6 -209 + 19x2 = 102x + -53 Reorder the terms: -209 + 19x2 = -53 + 102x Solving -209 + 19x2 = -53 + 102x Solving for variable 'x'. Reorder the terms: -209 + 53 + -102x + 19x2 = -53 + 102x + 53 + -102x Combine like terms: -209 + 53 = -156 -156 + -102x + 19x2 = -53 + 102x + 53 + -102x Reorder the terms: -156 + -102x + 19x2 = -53 + 53 + 102x + -102x Combine like terms: -53 + 53 = 0 -156 + -102x + 19x2 = 0 + 102x + -102x -156 + -102x + 19x2 = 102x + -102x Combine like terms: 102x + -102x = 0 -156 + -102x + 19x2 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -8.210526316 + -5.368421053x + x2 = 0 Move the constant term to the right: Add '8.210526316' to each side of the equation. -8.210526316 + -5.368421053x + 8.210526316 + x2 = 0 + 8.210526316 Reorder the terms: -8.210526316 + 8.210526316 + -5.368421053x + x2 = 0 + 8.210526316 Combine like terms: -8.210526316 + 8.210526316 = 0.000000000 0.000000000 + -5.368421053x + x2 = 0 + 8.210526316 -5.368421053x + x2 = 0 + 8.210526316 Combine like terms: 0 + 8.210526316 = 8.210526316 -5.368421053x + x2 = 8.210526316 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 = 8.210526316 + 7.204986153 Reorder the terms: 7.204986153 + -5.368421053x + x2 = 8.210526316 + 7.204986153 Combine like terms: 8.210526316 + 7.204986153 = 15.415512469 7.204986153 + -5.368421053x + x2 = 15.415512469 Factor a perfect square on the left side: (x + -2.684210527)(x + -2.684210527) = 15.415512469 Calculate the square root of the right side: 3.926259348 Break this problem into two subproblems by setting (x + -2.684210527) equal to 3.926259348 and -3.926259348.Subproblem 1
x + -2.684210527 = 3.926259348 Simplifying x + -2.684210527 = 3.926259348 Reorder the terms: -2.684210527 + x = 3.926259348 Solving -2.684210527 + x = 3.926259348 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 = 3.926259348 + 2.684210527 Combine like terms: -2.684210527 + 2.684210527 = 0.000000000 0.000000000 + x = 3.926259348 + 2.684210527 x = 3.926259348 + 2.684210527 Combine like terms: 3.926259348 + 2.684210527 = 6.610469875 x = 6.610469875 Simplifying x = 6.610469875Subproblem 2
x + -2.684210527 = -3.926259348 Simplifying x + -2.684210527 = -3.926259348 Reorder the terms: -2.684210527 + x = -3.926259348 Solving -2.684210527 + x = -3.926259348 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 = -3.926259348 + 2.684210527 Combine like terms: -2.684210527 + 2.684210527 = 0.000000000 0.000000000 + x = -3.926259348 + 2.684210527 x = -3.926259348 + 2.684210527 Combine like terms: -3.926259348 + 2.684210527 = -1.242048821 x = -1.242048821 Simplifying x = -1.242048821Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.610469875, -1.242048821}
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