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Simplifying 2x2 + -15x + -16 = 11 + -24x Reorder the terms: -16 + -15x + 2x2 = 11 + -24x Solving -16 + -15x + 2x2 = 11 + -24x Solving for variable 'x'. Reorder the terms: -16 + -11 + -15x + 24x + 2x2 = 11 + -24x + -11 + 24x Combine like terms: -16 + -11 = -27 -27 + -15x + 24x + 2x2 = 11 + -24x + -11 + 24x Combine like terms: -15x + 24x = 9x -27 + 9x + 2x2 = 11 + -24x + -11 + 24x Reorder the terms: -27 + 9x + 2x2 = 11 + -11 + -24x + 24x Combine like terms: 11 + -11 = 0 -27 + 9x + 2x2 = 0 + -24x + 24x -27 + 9x + 2x2 = -24x + 24x Combine like terms: -24x + 24x = 0 -27 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + 4.5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + 4.5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + 4.5x + x2 = 0 + 13.5 4.5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 4.5x + x2 = 13.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 13.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 13.5 + 5.0625 Combine like terms: 13.5 + 5.0625 = 18.5625 5.0625 + 4.5x + x2 = 18.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (x + 2.25) equal to 4.308421985 and -4.308421985.Subproblem 1
x + 2.25 = 4.308421985 Simplifying x + 2.25 = 4.308421985 Reorder the terms: 2.25 + x = 4.308421985 Solving 2.25 + x = 4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 4.308421985 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 4.308421985 + -2.25 x = 4.308421985 + -2.25 Combine like terms: 4.308421985 + -2.25 = 2.058421985 x = 2.058421985 Simplifying x = 2.058421985Subproblem 2
x + 2.25 = -4.308421985 Simplifying x + 2.25 = -4.308421985 Reorder the terms: 2.25 + x = -4.308421985 Solving 2.25 + x = -4.308421985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -4.308421985 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -4.308421985 + -2.25 x = -4.308421985 + -2.25 Combine like terms: -4.308421985 + -2.25 = -6.558421985 x = -6.558421985 Simplifying x = -6.558421985Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.058421985, -6.558421985}
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