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Simplifying 3x(2x + -33) + 4(54 + -2x) = 33 Reorder the terms: 3x(-33 + 2x) + 4(54 + -2x) = 33 (-33 * 3x + 2x * 3x) + 4(54 + -2x) = 33 (-99x + 6x2) + 4(54 + -2x) = 33 -99x + 6x2 + (54 * 4 + -2x * 4) = 33 -99x + 6x2 + (216 + -8x) = 33 Reorder the terms: 216 + -99x + -8x + 6x2 = 33 Combine like terms: -99x + -8x = -107x 216 + -107x + 6x2 = 33 Solving 216 + -107x + 6x2 = 33 Solving for variable 'x'. Reorder the terms: 216 + -33 + -107x + 6x2 = 33 + -33 Combine like terms: 216 + -33 = 183 183 + -107x + 6x2 = 33 + -33 Combine like terms: 33 + -33 = 0 183 + -107x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 30.5 + -17.83333333x + x2 = 0 Move the constant term to the right: Add '-30.5' to each side of the equation. 30.5 + -17.83333333x + -30.5 + x2 = 0 + -30.5 Reorder the terms: 30.5 + -30.5 + -17.83333333x + x2 = 0 + -30.5 Combine like terms: 30.5 + -30.5 = 0.0 0.0 + -17.83333333x + x2 = 0 + -30.5 -17.83333333x + x2 = 0 + -30.5 Combine like terms: 0 + -30.5 = -30.5 -17.83333333x + x2 = -30.5 The x term is -17.83333333x. Take half its coefficient (-8.916666665). Square it (79.50694441) and add it to both sides. Add '79.50694441' to each side of the equation. -17.83333333x + 79.50694441 + x2 = -30.5 + 79.50694441 Reorder the terms: 79.50694441 + -17.83333333x + x2 = -30.5 + 79.50694441 Combine like terms: -30.5 + 79.50694441 = 49.00694441 79.50694441 + -17.83333333x + x2 = 49.00694441 Factor a perfect square on the left side: (x + -8.916666665)(x + -8.916666665) = 49.00694441 Calculate the square root of the right side: 7.000496012 Break this problem into two subproblems by setting (x + -8.916666665) equal to 7.000496012 and -7.000496012.Subproblem 1
x + -8.916666665 = 7.000496012 Simplifying x + -8.916666665 = 7.000496012 Reorder the terms: -8.916666665 + x = 7.000496012 Solving -8.916666665 + x = 7.000496012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.916666665' to each side of the equation. -8.916666665 + 8.916666665 + x = 7.000496012 + 8.916666665 Combine like terms: -8.916666665 + 8.916666665 = 0.000000000 0.000000000 + x = 7.000496012 + 8.916666665 x = 7.000496012 + 8.916666665 Combine like terms: 7.000496012 + 8.916666665 = 15.917162677 x = 15.917162677 Simplifying x = 15.917162677Subproblem 2
x + -8.916666665 = -7.000496012 Simplifying x + -8.916666665 = -7.000496012 Reorder the terms: -8.916666665 + x = -7.000496012 Solving -8.916666665 + x = -7.000496012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.916666665' to each side of the equation. -8.916666665 + 8.916666665 + x = -7.000496012 + 8.916666665 Combine like terms: -8.916666665 + 8.916666665 = 0.000000000 0.000000000 + x = -7.000496012 + 8.916666665 x = -7.000496012 + 8.916666665 Combine like terms: -7.000496012 + 8.916666665 = 1.916170653 x = 1.916170653 Simplifying x = 1.916170653Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.917162677, 1.916170653}
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