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Simplifying 4x2 + -8x + -333 = 0 Reorder the terms: -333 + -8x + 4x2 = 0 Solving -333 + -8x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -83.25 + -2x + x2 = 0 Move the constant term to the right: Add '83.25' to each side of the equation. -83.25 + -2x + 83.25 + x2 = 0 + 83.25 Reorder the terms: -83.25 + 83.25 + -2x + x2 = 0 + 83.25 Combine like terms: -83.25 + 83.25 = 0.00 0.00 + -2x + x2 = 0 + 83.25 -2x + x2 = 0 + 83.25 Combine like terms: 0 + 83.25 = 83.25 -2x + x2 = 83.25 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 83.25 + 1 Reorder the terms: 1 + -2x + x2 = 83.25 + 1 Combine like terms: 83.25 + 1 = 84.25 1 + -2x + x2 = 84.25 Factor a perfect square on the left side: (x + -1)(x + -1) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (x + -1) equal to 9.178779875 and -9.178779875.Subproblem 1
x + -1 = 9.178779875 Simplifying x + -1 = 9.178779875 Reorder the terms: -1 + x = 9.178779875 Solving -1 + x = 9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 9.178779875 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.178779875 + 1 x = 9.178779875 + 1 Combine like terms: 9.178779875 + 1 = 10.178779875 x = 10.178779875 Simplifying x = 10.178779875Subproblem 2
x + -1 = -9.178779875 Simplifying x + -1 = -9.178779875 Reorder the terms: -1 + x = -9.178779875 Solving -1 + x = -9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -9.178779875 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.178779875 + 1 x = -9.178779875 + 1 Combine like terms: -9.178779875 + 1 = -8.178779875 x = -8.178779875 Simplifying x = -8.178779875Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.178779875, -8.178779875}
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