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Simplifying -16x2 + 34.92x + 3 = 10 Reorder the terms: 3 + 34.92x + -16x2 = 10 Solving 3 + 34.92x + -16x2 = 10 Solving for variable 'x'. Reorder the terms: 3 + -10 + 34.92x + -16x2 = 10 + -10 Combine like terms: 3 + -10 = -7 -7 + 34.92x + -16x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -7 + 34.92x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.4375 + -2.1825x + x2 = 0 Move the constant term to the right: Add '-0.4375' to each side of the equation. 0.4375 + -2.1825x + -0.4375 + x2 = 0 + -0.4375 Reorder the terms: 0.4375 + -0.4375 + -2.1825x + x2 = 0 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + -2.1825x + x2 = 0 + -0.4375 -2.1825x + x2 = 0 + -0.4375 Combine like terms: 0 + -0.4375 = -0.4375 -2.1825x + x2 = -0.4375 The x term is -2.1825x. Take half its coefficient (-1.09125). Square it (1.190826563) and add it to both sides. Add '1.190826563' to each side of the equation. -2.1825x + 1.190826563 + x2 = -0.4375 + 1.190826563 Reorder the terms: 1.190826563 + -2.1825x + x2 = -0.4375 + 1.190826563 Combine like terms: -0.4375 + 1.190826563 = 0.753326563 1.190826563 + -2.1825x + x2 = 0.753326563 Factor a perfect square on the left side: (x + -1.09125)(x + -1.09125) = 0.753326563 Calculate the square root of the right side: 0.867943871 Break this problem into two subproblems by setting (x + -1.09125) equal to 0.867943871 and -0.867943871.Subproblem 1
x + -1.09125 = 0.867943871 Simplifying x + -1.09125 = 0.867943871 Reorder the terms: -1.09125 + x = 0.867943871 Solving -1.09125 + x = 0.867943871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09125' to each side of the equation. -1.09125 + 1.09125 + x = 0.867943871 + 1.09125 Combine like terms: -1.09125 + 1.09125 = 0.00000 0.00000 + x = 0.867943871 + 1.09125 x = 0.867943871 + 1.09125 Combine like terms: 0.867943871 + 1.09125 = 1.959193871 x = 1.959193871 Simplifying x = 1.959193871Subproblem 2
x + -1.09125 = -0.867943871 Simplifying x + -1.09125 = -0.867943871 Reorder the terms: -1.09125 + x = -0.867943871 Solving -1.09125 + x = -0.867943871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.09125' to each side of the equation. -1.09125 + 1.09125 + x = -0.867943871 + 1.09125 Combine like terms: -1.09125 + 1.09125 = 0.00000 0.00000 + x = -0.867943871 + 1.09125 x = -0.867943871 + 1.09125 Combine like terms: -0.867943871 + 1.09125 = 0.223306129 x = 0.223306129 Simplifying x = 0.223306129Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.959193871, 0.223306129}
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