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Simplifying 8x2 + -23x + -48 = 0 Reorder the terms: -48 + -23x + 8x2 = 0 Solving -48 + -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'. -6 + -2.875x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -2.875x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -2.875x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2.875x + x2 = 0 + 6 -2.875x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2.875x + x2 = 6 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 = 6 + 2.06640625 Reorder the terms: 2.06640625 + -2.875x + x2 = 6 + 2.06640625 Combine like terms: 6 + 2.06640625 = 8.06640625 2.06640625 + -2.875x + x2 = 8.06640625 Factor a perfect square on the left side: (x + -1.4375)(x + -1.4375) = 8.06640625 Calculate the square root of the right side: 2.840141942 Break this problem into two subproblems by setting (x + -1.4375) equal to 2.840141942 and -2.840141942.Subproblem 1
x + -1.4375 = 2.840141942 Simplifying x + -1.4375 = 2.840141942 Reorder the terms: -1.4375 + x = 2.840141942 Solving -1.4375 + x = 2.840141942 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 = 2.840141942 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + x = 2.840141942 + 1.4375 x = 2.840141942 + 1.4375 Combine like terms: 2.840141942 + 1.4375 = 4.277641942 x = 4.277641942 Simplifying x = 4.277641942Subproblem 2
x + -1.4375 = -2.840141942 Simplifying x + -1.4375 = -2.840141942 Reorder the terms: -1.4375 + x = -2.840141942 Solving -1.4375 + x = -2.840141942 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 = -2.840141942 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + x = -2.840141942 + 1.4375 x = -2.840141942 + 1.4375 Combine like terms: -2.840141942 + 1.4375 = -1.402641942 x = -1.402641942 Simplifying x = -1.402641942Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.277641942, -1.402641942}
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