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Simplifying 8x2 + -28x + -23 = 0 Reorder the terms: -23 + -28x + 8x2 = 0 Solving -23 + -28x + 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'. -2.875 + -3.5x + x2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + -3.5x + 2.875 + x2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + -3.5x + x2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + -3.5x + x2 = 0 + 2.875 -3.5x + x2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 -3.5x + x2 = 2.875 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 2.875 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 2.875 + 3.0625 Combine like terms: 2.875 + 3.0625 = 5.9375 3.0625 + -3.5x + x2 = 5.9375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 5.9375 Calculate the square root of the right side: 2.436698586 Break this problem into two subproblems by setting (x + -1.75) equal to 2.436698586 and -2.436698586.Subproblem 1
x + -1.75 = 2.436698586 Simplifying x + -1.75 = 2.436698586 Reorder the terms: -1.75 + x = 2.436698586 Solving -1.75 + x = 2.436698586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 2.436698586 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.436698586 + 1.75 x = 2.436698586 + 1.75 Combine like terms: 2.436698586 + 1.75 = 4.186698586 x = 4.186698586 Simplifying x = 4.186698586Subproblem 2
x + -1.75 = -2.436698586 Simplifying x + -1.75 = -2.436698586 Reorder the terms: -1.75 + x = -2.436698586 Solving -1.75 + x = -2.436698586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -2.436698586 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.436698586 + 1.75 x = -2.436698586 + 1.75 Combine like terms: -2.436698586 + 1.75 = -0.686698586 x = -0.686698586 Simplifying x = -0.686698586Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.186698586, -0.686698586}
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