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Simplifying 8x2 + (-34) * x + -1(-9) = 0 Multiply -1 * -9 8x2 + -34x + 9 = 0 Reorder the terms: 9 + -34x + 8x2 = 0 Solving 9 + -34x + 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'. 1.125 + -4.25x + x2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -4.25x + -1.125 + x2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -4.25x + x2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -4.25x + x2 = 0 + -1.125 -4.25x + x2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -4.25x + x2 = -1.125 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = -1.125 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = -1.125 + 4.515625 Combine like terms: -1.125 + 4.515625 = 3.390625 4.515625 + -4.25x + x2 = 3.390625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (x + -2.125) equal to 1.841364983 and -1.841364983.Subproblem 1
x + -2.125 = 1.841364983 Simplifying x + -2.125 = 1.841364983 Reorder the terms: -2.125 + x = 1.841364983 Solving -2.125 + x = 1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 1.841364983 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 1.841364983 + 2.125 x = 1.841364983 + 2.125 Combine like terms: 1.841364983 + 2.125 = 3.966364983 x = 3.966364983 Simplifying x = 3.966364983Subproblem 2
x + -2.125 = -1.841364983 Simplifying x + -2.125 = -1.841364983 Reorder the terms: -2.125 + x = -1.841364983 Solving -2.125 + x = -1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -1.841364983 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -1.841364983 + 2.125 x = -1.841364983 + 2.125 Combine like terms: -1.841364983 + 2.125 = 0.283635017 x = 0.283635017 Simplifying x = 0.283635017Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.966364983, 0.283635017}
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