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Simplifying 2x2 + -8x + -165 = 0 Reorder the terms: -165 + -8x + 2x2 = 0 Solving -165 + -8x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -82.5 + -4x + x2 = 0 Move the constant term to the right: Add '82.5' to each side of the equation. -82.5 + -4x + 82.5 + x2 = 0 + 82.5 Reorder the terms: -82.5 + 82.5 + -4x + x2 = 0 + 82.5 Combine like terms: -82.5 + 82.5 = 0.0 0.0 + -4x + x2 = 0 + 82.5 -4x + x2 = 0 + 82.5 Combine like terms: 0 + 82.5 = 82.5 -4x + x2 = 82.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 82.5 + 4 Reorder the terms: 4 + -4x + x2 = 82.5 + 4 Combine like terms: 82.5 + 4 = 86.5 4 + -4x + x2 = 86.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 86.5 Calculate the square root of the right side: 9.300537619 Break this problem into two subproblems by setting (x + -2) equal to 9.300537619 and -9.300537619.Subproblem 1
x + -2 = 9.300537619 Simplifying x + -2 = 9.300537619 Reorder the terms: -2 + x = 9.300537619 Solving -2 + x = 9.300537619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 9.300537619 + 2 Combine like terms: -2 + 2 = 0 0 + x = 9.300537619 + 2 x = 9.300537619 + 2 Combine like terms: 9.300537619 + 2 = 11.300537619 x = 11.300537619 Simplifying x = 11.300537619Subproblem 2
x + -2 = -9.300537619 Simplifying x + -2 = -9.300537619 Reorder the terms: -2 + x = -9.300537619 Solving -2 + x = -9.300537619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -9.300537619 + 2 Combine like terms: -2 + 2 = 0 0 + x = -9.300537619 + 2 x = -9.300537619 + 2 Combine like terms: -9.300537619 + 2 = -7.300537619 x = -7.300537619 Simplifying x = -7.300537619Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.300537619, -7.300537619}
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