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Simplifying 28x2 + -11x + -62 = 0 Reorder the terms: -62 + -11x + 28x2 = 0 Solving -62 + -11x + 28x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -2.214285714 + -0.3928571429x + x2 = 0 Move the constant term to the right: Add '2.214285714' to each side of the equation. -2.214285714 + -0.3928571429x + 2.214285714 + x2 = 0 + 2.214285714 Reorder the terms: -2.214285714 + 2.214285714 + -0.3928571429x + x2 = 0 + 2.214285714 Combine like terms: -2.214285714 + 2.214285714 = 0.000000000 0.000000000 + -0.3928571429x + x2 = 0 + 2.214285714 -0.3928571429x + x2 = 0 + 2.214285714 Combine like terms: 0 + 2.214285714 = 2.214285714 -0.3928571429x + x2 = 2.214285714 The x term is -0.3928571429x. Take half its coefficient (-0.1964285715). Square it (0.03858418370) and add it to both sides. Add '0.03858418370' to each side of the equation. -0.3928571429x + 0.03858418370 + x2 = 2.214285714 + 0.03858418370 Reorder the terms: 0.03858418370 + -0.3928571429x + x2 = 2.214285714 + 0.03858418370 Combine like terms: 2.214285714 + 0.03858418370 = 2.2528698977 0.03858418370 + -0.3928571429x + x2 = 2.2528698977 Factor a perfect square on the left side: (x + -0.1964285715)(x + -0.1964285715) = 2.2528698977 Calculate the square root of the right side: 1.500956328 Break this problem into two subproblems by setting (x + -0.1964285715) equal to 1.500956328 and -1.500956328.Subproblem 1
x + -0.1964285715 = 1.500956328 Simplifying x + -0.1964285715 = 1.500956328 Reorder the terms: -0.1964285715 + x = 1.500956328 Solving -0.1964285715 + x = 1.500956328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1964285715' to each side of the equation. -0.1964285715 + 0.1964285715 + x = 1.500956328 + 0.1964285715 Combine like terms: -0.1964285715 + 0.1964285715 = 0.0000000000 0.0000000000 + x = 1.500956328 + 0.1964285715 x = 1.500956328 + 0.1964285715 Combine like terms: 1.500956328 + 0.1964285715 = 1.6973848995 x = 1.6973848995 Simplifying x = 1.6973848995Subproblem 2
x + -0.1964285715 = -1.500956328 Simplifying x + -0.1964285715 = -1.500956328 Reorder the terms: -0.1964285715 + x = -1.500956328 Solving -0.1964285715 + x = -1.500956328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1964285715' to each side of the equation. -0.1964285715 + 0.1964285715 + x = -1.500956328 + 0.1964285715 Combine like terms: -0.1964285715 + 0.1964285715 = 0.0000000000 0.0000000000 + x = -1.500956328 + 0.1964285715 x = -1.500956328 + 0.1964285715 Combine like terms: -1.500956328 + 0.1964285715 = -1.3045277565 x = -1.3045277565 Simplifying x = -1.3045277565Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6973848995, -1.3045277565}
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