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Simplifying 8x2 + -23x + 3 = 0 Reorder the terms: 3 + -23x + 8x2 = 0 Solving 3 + -23x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + -2.875x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -2.875x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -2.875x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -2.875x + x2 = 0 + -0.375 -2.875x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -2.875x + x2 = -0.375 The x term is -2.875x. Take half its coefficient (-1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. -2.875x + 2.06640625 + x2 = -0.375 + 2.06640625 Reorder the terms: 2.06640625 + -2.875x + x2 = -0.375 + 2.06640625 Combine like terms: -0.375 + 2.06640625 = 1.69140625 2.06640625 + -2.875x + x2 = 1.69140625 Factor a perfect square on the left side: (x + -1.4375)(x + -1.4375) = 1.69140625 Calculate the square root of the right side: 1.300540753 Break this problem into two subproblems by setting (x + -1.4375) equal to 1.300540753 and -1.300540753.Subproblem 1
x + -1.4375 = 1.300540753 Simplifying x + -1.4375 = 1.300540753 Reorder the terms: -1.4375 + x = 1.300540753 Solving -1.4375 + x = 1.300540753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + x = 1.300540753 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + x = 1.300540753 + 1.4375 x = 1.300540753 + 1.4375 Combine like terms: 1.300540753 + 1.4375 = 2.738040753 x = 2.738040753 Simplifying x = 2.738040753Subproblem 2
x + -1.4375 = -1.300540753 Simplifying x + -1.4375 = -1.300540753 Reorder the terms: -1.4375 + x = -1.300540753 Solving -1.4375 + x = -1.300540753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + x = -1.300540753 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + x = -1.300540753 + 1.4375 x = -1.300540753 + 1.4375 Combine like terms: -1.300540753 + 1.4375 = 0.136959247 x = 0.136959247 Simplifying x = 0.136959247Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.738040753, 0.136959247}
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