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Simplifying 8x2 + 9x + -160 = 0 Reorder the terms: -160 + 9x + 8x2 = 0 Solving -160 + 9x + 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'. -20 + 1.125x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 1.125x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 1.125x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 1.125x + x2 = 0 + 20 1.125x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 1.125x + x2 = 20 The x term is 1.125x. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125x + 0.31640625 + x2 = 20 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 20 + 0.31640625 Combine like terms: 20 + 0.31640625 = 20.31640625 0.31640625 + 1.125x + x2 = 20.31640625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 20.31640625 Calculate the square root of the right side: 4.507372433 Break this problem into two subproblems by setting (x + 0.5625) equal to 4.507372433 and -4.507372433.Subproblem 1
x + 0.5625 = 4.507372433 Simplifying x + 0.5625 = 4.507372433 Reorder the terms: 0.5625 + x = 4.507372433 Solving 0.5625 + x = 4.507372433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = 4.507372433 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 4.507372433 + -0.5625 x = 4.507372433 + -0.5625 Combine like terms: 4.507372433 + -0.5625 = 3.944872433 x = 3.944872433 Simplifying x = 3.944872433Subproblem 2
x + 0.5625 = -4.507372433 Simplifying x + 0.5625 = -4.507372433 Reorder the terms: 0.5625 + x = -4.507372433 Solving 0.5625 + x = -4.507372433 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + x = -4.507372433 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -4.507372433 + -0.5625 x = -4.507372433 + -0.5625 Combine like terms: -4.507372433 + -0.5625 = -5.069872433 x = -5.069872433 Simplifying x = -5.069872433Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.944872433, -5.069872433}
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