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Simplifying 8x2 + -30x + -1 = 0 Reorder the terms: -1 + -30x + 8x2 = 0 Solving -1 + -30x + 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'. -0.125 + -3.75x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -3.75x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -3.75x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -3.75x + x2 = 0 + 0.125 -3.75x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -3.75x + x2 = 0.125 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 0.125 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 0.125 + 3.515625 Combine like terms: 0.125 + 3.515625 = 3.640625 3.515625 + -3.75x + x2 = 3.640625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 3.640625 Calculate the square root of the right side: 1.90804219 Break this problem into two subproblems by setting (x + -1.875) equal to 1.90804219 and -1.90804219.Subproblem 1
x + -1.875 = 1.90804219 Simplifying x + -1.875 = 1.90804219 Reorder the terms: -1.875 + x = 1.90804219 Solving -1.875 + x = 1.90804219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 1.90804219 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 1.90804219 + 1.875 x = 1.90804219 + 1.875 Combine like terms: 1.90804219 + 1.875 = 3.78304219 x = 3.78304219 Simplifying x = 3.78304219Subproblem 2
x + -1.875 = -1.90804219 Simplifying x + -1.875 = -1.90804219 Reorder the terms: -1.875 + x = -1.90804219 Solving -1.875 + x = -1.90804219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -1.90804219 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -1.90804219 + 1.875 x = -1.90804219 + 1.875 Combine like terms: -1.90804219 + 1.875 = -0.03304219 x = -0.03304219 Simplifying x = -0.03304219Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.78304219, -0.03304219}
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