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Simplifying 13x2 + -190x + -96 = 0 Reorder the terms: -96 + -190x + 13x2 = 0 Solving -96 + -190x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -7.384615385 + -14.61538462x + x2 = 0 Move the constant term to the right: Add '7.384615385' to each side of the equation. -7.384615385 + -14.61538462x + 7.384615385 + x2 = 0 + 7.384615385 Reorder the terms: -7.384615385 + 7.384615385 + -14.61538462x + x2 = 0 + 7.384615385 Combine like terms: -7.384615385 + 7.384615385 = 0.000000000 0.000000000 + -14.61538462x + x2 = 0 + 7.384615385 -14.61538462x + x2 = 0 + 7.384615385 Combine like terms: 0 + 7.384615385 = 7.384615385 -14.61538462x + x2 = 7.384615385 The x term is -14.61538462x. Take half its coefficient (-7.30769231). Square it (53.40236690) and add it to both sides. Add '53.40236690' to each side of the equation. -14.61538462x + 53.40236690 + x2 = 7.384615385 + 53.40236690 Reorder the terms: 53.40236690 + -14.61538462x + x2 = 7.384615385 + 53.40236690 Combine like terms: 7.384615385 + 53.40236690 = 60.786982285 53.40236690 + -14.61538462x + x2 = 60.786982285 Factor a perfect square on the left side: (x + -7.30769231)(x + -7.30769231) = 60.786982285 Calculate the square root of the right side: 7.796600688 Break this problem into two subproblems by setting (x + -7.30769231) equal to 7.796600688 and -7.796600688.Subproblem 1
x + -7.30769231 = 7.796600688 Simplifying x + -7.30769231 = 7.796600688 Reorder the terms: -7.30769231 + x = 7.796600688 Solving -7.30769231 + x = 7.796600688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.30769231' to each side of the equation. -7.30769231 + 7.30769231 + x = 7.796600688 + 7.30769231 Combine like terms: -7.30769231 + 7.30769231 = 0.00000000 0.00000000 + x = 7.796600688 + 7.30769231 x = 7.796600688 + 7.30769231 Combine like terms: 7.796600688 + 7.30769231 = 15.104292998 x = 15.104292998 Simplifying x = 15.104292998Subproblem 2
x + -7.30769231 = -7.796600688 Simplifying x + -7.30769231 = -7.796600688 Reorder the terms: -7.30769231 + x = -7.796600688 Solving -7.30769231 + x = -7.796600688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.30769231' to each side of the equation. -7.30769231 + 7.30769231 + x = -7.796600688 + 7.30769231 Combine like terms: -7.30769231 + 7.30769231 = 0.00000000 0.00000000 + x = -7.796600688 + 7.30769231 x = -7.796600688 + 7.30769231 Combine like terms: -7.796600688 + 7.30769231 = -0.488908378 x = -0.488908378 Simplifying x = -0.488908378Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.104292998, -0.488908378}
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