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Simplifying 8X2 + 20X + -11 = 0 Reorder the terms: -11 + 20X + 8X2 = 0 Solving -11 + 20X + 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'. -1.375 + 2.5X + X2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 2.5X + 1.375 + X2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 2.5X + X2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 2.5X + X2 = 0 + 1.375 2.5X + X2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 2.5X + X2 = 1.375 The X term is 2.5X. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5X + 1.5625 + X2 = 1.375 + 1.5625 Reorder the terms: 1.5625 + 2.5X + X2 = 1.375 + 1.5625 Combine like terms: 1.375 + 1.5625 = 2.9375 1.5625 + 2.5X + X2 = 2.9375 Factor a perfect square on the left side: (X + 1.25)(X + 1.25) = 2.9375 Calculate the square root of the right side: 1.71391365 Break this problem into two subproblems by setting (X + 1.25) equal to 1.71391365 and -1.71391365.Subproblem 1
X + 1.25 = 1.71391365 Simplifying X + 1.25 = 1.71391365 Reorder the terms: 1.25 + X = 1.71391365 Solving 1.25 + X = 1.71391365 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + X = 1.71391365 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + X = 1.71391365 + -1.25 X = 1.71391365 + -1.25 Combine like terms: 1.71391365 + -1.25 = 0.46391365 X = 0.46391365 Simplifying X = 0.46391365Subproblem 2
X + 1.25 = -1.71391365 Simplifying X + 1.25 = -1.71391365 Reorder the terms: 1.25 + X = -1.71391365 Solving 1.25 + X = -1.71391365 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + X = -1.71391365 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + X = -1.71391365 + -1.25 X = -1.71391365 + -1.25 Combine like terms: -1.71391365 + -1.25 = -2.96391365 X = -2.96391365 Simplifying X = -2.96391365Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.46391365, -2.96391365}
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