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Simplifying 8x2 + -17x + -30 = 0 Reorder the terms: -30 + -17x + 8x2 = 0 Solving -30 + -17x + 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'. -3.75 + -2.125x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -2.125x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -2.125x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -2.125x + x2 = 0 + 3.75 -2.125x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -2.125x + x2 = 3.75 The x term is -2.125x. Take half its coefficient (-1.0625). Square it (1.12890625) and add it to both sides. Add '1.12890625' to each side of the equation. -2.125x + 1.12890625 + x2 = 3.75 + 1.12890625 Reorder the terms: 1.12890625 + -2.125x + x2 = 3.75 + 1.12890625 Combine like terms: 3.75 + 1.12890625 = 4.87890625 1.12890625 + -2.125x + x2 = 4.87890625 Factor a perfect square on the left side: (x + -1.0625)(x + -1.0625) = 4.87890625 Calculate the square root of the right side: 2.208824631 Break this problem into two subproblems by setting (x + -1.0625) equal to 2.208824631 and -2.208824631.Subproblem 1
x + -1.0625 = 2.208824631 Simplifying x + -1.0625 = 2.208824631 Reorder the terms: -1.0625 + x = 2.208824631 Solving -1.0625 + x = 2.208824631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = 2.208824631 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = 2.208824631 + 1.0625 x = 2.208824631 + 1.0625 Combine like terms: 2.208824631 + 1.0625 = 3.271324631 x = 3.271324631 Simplifying x = 3.271324631Subproblem 2
x + -1.0625 = -2.208824631 Simplifying x + -1.0625 = -2.208824631 Reorder the terms: -1.0625 + x = -2.208824631 Solving -1.0625 + x = -2.208824631 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.0625' to each side of the equation. -1.0625 + 1.0625 + x = -2.208824631 + 1.0625 Combine like terms: -1.0625 + 1.0625 = 0.0000 0.0000 + x = -2.208824631 + 1.0625 x = -2.208824631 + 1.0625 Combine like terms: -2.208824631 + 1.0625 = -1.146324631 x = -1.146324631 Simplifying x = -1.146324631Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.271324631, -1.146324631}
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