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Simplifying 8x2 + -32x + -247 = 0 Reorder the terms: -247 + -32x + 8x2 = 0 Solving -247 + -32x + 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'. -30.875 + -4x + x2 = 0 Move the constant term to the right: Add '30.875' to each side of the equation. -30.875 + -4x + 30.875 + x2 = 0 + 30.875 Reorder the terms: -30.875 + 30.875 + -4x + x2 = 0 + 30.875 Combine like terms: -30.875 + 30.875 = 0.000 0.000 + -4x + x2 = 0 + 30.875 -4x + x2 = 0 + 30.875 Combine like terms: 0 + 30.875 = 30.875 -4x + x2 = 30.875 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 = 30.875 + 4 Reorder the terms: 4 + -4x + x2 = 30.875 + 4 Combine like terms: 30.875 + 4 = 34.875 4 + -4x + x2 = 34.875 Factor a perfect square on the left side: (x + -2)(x + -2) = 34.875 Calculate the square root of the right side: 5.905505906 Break this problem into two subproblems by setting (x + -2) equal to 5.905505906 and -5.905505906.Subproblem 1
x + -2 = 5.905505906 Simplifying x + -2 = 5.905505906 Reorder the terms: -2 + x = 5.905505906 Solving -2 + x = 5.905505906 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 = 5.905505906 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.905505906 + 2 x = 5.905505906 + 2 Combine like terms: 5.905505906 + 2 = 7.905505906 x = 7.905505906 Simplifying x = 7.905505906Subproblem 2
x + -2 = -5.905505906 Simplifying x + -2 = -5.905505906 Reorder the terms: -2 + x = -5.905505906 Solving -2 + x = -5.905505906 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 = -5.905505906 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.905505906 + 2 x = -5.905505906 + 2 Combine like terms: -5.905505906 + 2 = -3.905505906 x = -3.905505906 Simplifying x = -3.905505906Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.905505906, -3.905505906}
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