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Simplifying 2x2 + -24x = 33 Reorder the terms: -24x + 2x2 = 33 Solving -24x + 2x2 = 33 Solving for variable 'x'. Reorder the terms: -33 + -24x + 2x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + -24x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -16.5 + -12x + x2 = 0 Move the constant term to the right: Add '16.5' to each side of the equation. -16.5 + -12x + 16.5 + x2 = 0 + 16.5 Reorder the terms: -16.5 + 16.5 + -12x + x2 = 0 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + -12x + x2 = 0 + 16.5 -12x + x2 = 0 + 16.5 Combine like terms: 0 + 16.5 = 16.5 -12x + x2 = 16.5 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 16.5 + 36 Reorder the terms: 36 + -12x + x2 = 16.5 + 36 Combine like terms: 16.5 + 36 = 52.5 36 + -12x + x2 = 52.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 52.5 Calculate the square root of the right side: 7.245688373 Break this problem into two subproblems by setting (x + -6) equal to 7.245688373 and -7.245688373.Subproblem 1
x + -6 = 7.245688373 Simplifying x + -6 = 7.245688373 Reorder the terms: -6 + x = 7.245688373 Solving -6 + x = 7.245688373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.245688373 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.245688373 + 6 x = 7.245688373 + 6 Combine like terms: 7.245688373 + 6 = 13.245688373 x = 13.245688373 Simplifying x = 13.245688373Subproblem 2
x + -6 = -7.245688373 Simplifying x + -6 = -7.245688373 Reorder the terms: -6 + x = -7.245688373 Solving -6 + x = -7.245688373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.245688373 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.245688373 + 6 x = -7.245688373 + 6 Combine like terms: -7.245688373 + 6 = -1.245688373 x = -1.245688373 Simplifying x = -1.245688373Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.245688373, -1.245688373}
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