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Simplifying 19x2 + -140x + -180 = 0 Reorder the terms: -180 + -140x + 19x2 = 0 Solving -180 + -140x + 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'. -9.473684211 + -7.368421053x + x2 = 0 Move the constant term to the right: Add '9.473684211' to each side of the equation. -9.473684211 + -7.368421053x + 9.473684211 + x2 = 0 + 9.473684211 Reorder the terms: -9.473684211 + 9.473684211 + -7.368421053x + x2 = 0 + 9.473684211 Combine like terms: -9.473684211 + 9.473684211 = 0.000000000 0.000000000 + -7.368421053x + x2 = 0 + 9.473684211 -7.368421053x + x2 = 0 + 9.473684211 Combine like terms: 0 + 9.473684211 = 9.473684211 -7.368421053x + x2 = 9.473684211 The x term is -7.368421053x. Take half its coefficient (-3.684210527). Square it (13.57340721) and add it to both sides. Add '13.57340721' to each side of the equation. -7.368421053x + 13.57340721 + x2 = 9.473684211 + 13.57340721 Reorder the terms: 13.57340721 + -7.368421053x + x2 = 9.473684211 + 13.57340721 Combine like terms: 9.473684211 + 13.57340721 = 23.047091421 13.57340721 + -7.368421053x + x2 = 23.047091421 Factor a perfect square on the left side: (x + -3.684210527)(x + -3.684210527) = 23.047091421 Calculate the square root of the right side: 4.800738633 Break this problem into two subproblems by setting (x + -3.684210527) equal to 4.800738633 and -4.800738633.Subproblem 1
x + -3.684210527 = 4.800738633 Simplifying x + -3.684210527 = 4.800738633 Reorder the terms: -3.684210527 + x = 4.800738633 Solving -3.684210527 + x = 4.800738633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.684210527' to each side of the equation. -3.684210527 + 3.684210527 + x = 4.800738633 + 3.684210527 Combine like terms: -3.684210527 + 3.684210527 = 0.000000000 0.000000000 + x = 4.800738633 + 3.684210527 x = 4.800738633 + 3.684210527 Combine like terms: 4.800738633 + 3.684210527 = 8.48494916 x = 8.48494916 Simplifying x = 8.48494916Subproblem 2
x + -3.684210527 = -4.800738633 Simplifying x + -3.684210527 = -4.800738633 Reorder the terms: -3.684210527 + x = -4.800738633 Solving -3.684210527 + x = -4.800738633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.684210527' to each side of the equation. -3.684210527 + 3.684210527 + x = -4.800738633 + 3.684210527 Combine like terms: -3.684210527 + 3.684210527 = 0.000000000 0.000000000 + x = -4.800738633 + 3.684210527 x = -4.800738633 + 3.684210527 Combine like terms: -4.800738633 + 3.684210527 = -1.116528106 x = -1.116528106 Simplifying x = -1.116528106Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.48494916, -1.116528106}
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