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Simplifying 8x(x) + 24x = -17 Multiply x * x 8x2 + 24x = -17 Reorder the terms: 24x + 8x2 = -17 Solving 24x + 8x2 = -17 Solving for variable 'x'. Reorder the terms: 17 + 24x + 8x2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + 24x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.125 + 3x + x2 = 0 Move the constant term to the right: Add '-2.125' to each side of the equation. 2.125 + 3x + -2.125 + x2 = 0 + -2.125 Reorder the terms: 2.125 + -2.125 + 3x + x2 = 0 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + 3x + x2 = 0 + -2.125 3x + x2 = 0 + -2.125 Combine like terms: 0 + -2.125 = -2.125 3x + x2 = -2.125 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 = -2.125 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -2.125 + 2.25 Combine like terms: -2.125 + 2.25 = 0.125 2.25 + 3x + x2 = 0.125 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (x + 1.5) equal to 0.353553391 and -0.353553391.Subproblem 1
x + 1.5 = 0.353553391 Simplifying x + 1.5 = 0.353553391 Reorder the terms: 1.5 + x = 0.353553391 Solving 1.5 + x = 0.353553391 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 = 0.353553391 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.353553391 + -1.5 x = 0.353553391 + -1.5 Combine like terms: 0.353553391 + -1.5 = -1.146446609 x = -1.146446609 Simplifying x = -1.146446609Subproblem 2
x + 1.5 = -0.353553391 Simplifying x + 1.5 = -0.353553391 Reorder the terms: 1.5 + x = -0.353553391 Solving 1.5 + x = -0.353553391 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 = -0.353553391 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.353553391 + -1.5 x = -0.353553391 + -1.5 Combine like terms: -0.353553391 + -1.5 = -1.853553391 x = -1.853553391 Simplifying x = -1.853553391Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.146446609, -1.853553391}
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