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Simplifying 8x(x + -3) = 23 Reorder the terms: 8x(-3 + x) = 23 (-3 * 8x + x * 8x) = 23 (-24x + 8x2) = 23 Solving -24x + 8x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + -24x + 8x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -24x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.875 + -3x + x2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + -3x + 2.875 + x2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + -3x + x2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + -3x + x2 = 0 + 2.875 -3x + x2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 -3x + x2 = 2.875 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 2.875 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 2.875 + 2.25 Combine like terms: 2.875 + 2.25 = 5.125 2.25 + -3x + x2 = 5.125 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 5.125 Calculate the square root of the right side: 2.263846285 Break this problem into two subproblems by setting (x + -1.5) equal to 2.263846285 and -2.263846285.Subproblem 1
x + -1.5 = 2.263846285 Simplifying x + -1.5 = 2.263846285 Reorder the terms: -1.5 + x = 2.263846285 Solving -1.5 + x = 2.263846285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.263846285 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.263846285 + 1.5 x = 2.263846285 + 1.5 Combine like terms: 2.263846285 + 1.5 = 3.763846285 x = 3.763846285 Simplifying x = 3.763846285Subproblem 2
x + -1.5 = -2.263846285 Simplifying x + -1.5 = -2.263846285 Reorder the terms: -1.5 + x = -2.263846285 Solving -1.5 + x = -2.263846285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.263846285 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.263846285 + 1.5 x = -2.263846285 + 1.5 Combine like terms: -2.263846285 + 1.5 = -0.763846285 x = -0.763846285 Simplifying x = -0.763846285Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.763846285, -0.763846285}
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