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Simplifying 24x2 + -36x + -287 = 0 Reorder the terms: -287 + -36x + 24x2 = 0 Solving -287 + -36x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -11.95833333 + -1.5x + x2 = 0 Move the constant term to the right: Add '11.95833333' to each side of the equation. -11.95833333 + -1.5x + 11.95833333 + x2 = 0 + 11.95833333 Reorder the terms: -11.95833333 + 11.95833333 + -1.5x + x2 = 0 + 11.95833333 Combine like terms: -11.95833333 + 11.95833333 = 0.00000000 0.00000000 + -1.5x + x2 = 0 + 11.95833333 -1.5x + x2 = 0 + 11.95833333 Combine like terms: 0 + 11.95833333 = 11.95833333 -1.5x + x2 = 11.95833333 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 11.95833333 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 11.95833333 + 0.5625 Combine like terms: 11.95833333 + 0.5625 = 12.52083333 0.5625 + -1.5x + x2 = 12.52083333 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 12.52083333 Calculate the square root of the right side: 3.538478957 Break this problem into two subproblems by setting (x + -0.75) equal to 3.538478957 and -3.538478957.Subproblem 1
x + -0.75 = 3.538478957 Simplifying x + -0.75 = 3.538478957 Reorder the terms: -0.75 + x = 3.538478957 Solving -0.75 + x = 3.538478957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 3.538478957 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 3.538478957 + 0.75 x = 3.538478957 + 0.75 Combine like terms: 3.538478957 + 0.75 = 4.288478957 x = 4.288478957 Simplifying x = 4.288478957Subproblem 2
x + -0.75 = -3.538478957 Simplifying x + -0.75 = -3.538478957 Reorder the terms: -0.75 + x = -3.538478957 Solving -0.75 + x = -3.538478957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -3.538478957 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -3.538478957 + 0.75 x = -3.538478957 + 0.75 Combine like terms: -3.538478957 + 0.75 = -2.788478957 x = -2.788478957 Simplifying x = -2.788478957Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.288478957, -2.788478957}
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