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Simplifying 13X2 + -3X + -60 = 0 Reorder the terms: -60 + -3X + 13X2 = 0 Solving -60 + -3X + 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'. -4.615384615 + -0.2307692308X + X2 = 0 Move the constant term to the right: Add '4.615384615' to each side of the equation. -4.615384615 + -0.2307692308X + 4.615384615 + X2 = 0 + 4.615384615 Reorder the terms: -4.615384615 + 4.615384615 + -0.2307692308X + X2 = 0 + 4.615384615 Combine like terms: -4.615384615 + 4.615384615 = 0.000000000 0.000000000 + -0.2307692308X + X2 = 0 + 4.615384615 -0.2307692308X + X2 = 0 + 4.615384615 Combine like terms: 0 + 4.615384615 = 4.615384615 -0.2307692308X + X2 = 4.615384615 The X term is -0.2307692308X. Take half its coefficient (-0.1153846154). Square it (0.01331360947) and add it to both sides. Add '0.01331360947' to each side of the equation. -0.2307692308X + 0.01331360947 + X2 = 4.615384615 + 0.01331360947 Reorder the terms: 0.01331360947 + -0.2307692308X + X2 = 4.615384615 + 0.01331360947 Combine like terms: 4.615384615 + 0.01331360947 = 4.62869822447 0.01331360947 + -0.2307692308X + X2 = 4.62869822447 Factor a perfect square on the left side: (X + -0.1153846154)(X + -0.1153846154) = 4.62869822447 Calculate the square root of the right side: 2.151440965 Break this problem into two subproblems by setting (X + -0.1153846154) equal to 2.151440965 and -2.151440965.Subproblem 1
X + -0.1153846154 = 2.151440965 Simplifying X + -0.1153846154 = 2.151440965 Reorder the terms: -0.1153846154 + X = 2.151440965 Solving -0.1153846154 + X = 2.151440965 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.1153846154 + X = 2.151440965 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + X = 2.151440965 + 0.1153846154 X = 2.151440965 + 0.1153846154 Combine like terms: 2.151440965 + 0.1153846154 = 2.2668255804 X = 2.2668255804 Simplifying X = 2.2668255804Subproblem 2
X + -0.1153846154 = -2.151440965 Simplifying X + -0.1153846154 = -2.151440965 Reorder the terms: -0.1153846154 + X = -2.151440965 Solving -0.1153846154 + X = -2.151440965 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.1153846154' to each side of the equation. -0.1153846154 + 0.1153846154 + X = -2.151440965 + 0.1153846154 Combine like terms: -0.1153846154 + 0.1153846154 = 0.0000000000 0.0000000000 + X = -2.151440965 + 0.1153846154 X = -2.151440965 + 0.1153846154 Combine like terms: -2.151440965 + 0.1153846154 = -2.0360563496 X = -2.0360563496 Simplifying X = -2.0360563496Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.2668255804, -2.0360563496}
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