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Simplifying 3x + 4x + -2 + 2(3x + -45) * x + -4 = 56 Reorder the terms: 3x + 4x + -2 + 2(-45 + 3x) * x + -4 = 56 Reorder the terms for easier multiplication: 3x + 4x + -2 + 2x(-45 + 3x) + -4 = 56 3x + 4x + -2 + (-45 * 2x + 3x * 2x) + -4 = 56 3x + 4x + -2 + (-90x + 6x2) + -4 = 56 Reorder the terms: -2 + -4 + 3x + 4x + -90x + 6x2 = 56 Combine like terms: -2 + -4 = -6 -6 + 3x + 4x + -90x + 6x2 = 56 Combine like terms: 3x + 4x = 7x -6 + 7x + -90x + 6x2 = 56 Combine like terms: 7x + -90x = -83x -6 + -83x + 6x2 = 56 Solving -6 + -83x + 6x2 = 56 Solving for variable 'x'. Reorder the terms: -6 + -56 + -83x + 6x2 = 56 + -56 Combine like terms: -6 + -56 = -62 -62 + -83x + 6x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -62 + -83x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -10.33333333 + -13.83333333x + x2 = 0 Move the constant term to the right: Add '10.33333333' to each side of the equation. -10.33333333 + -13.83333333x + 10.33333333 + x2 = 0 + 10.33333333 Reorder the terms: -10.33333333 + 10.33333333 + -13.83333333x + x2 = 0 + 10.33333333 Combine like terms: -10.33333333 + 10.33333333 = 0.00000000 0.00000000 + -13.83333333x + x2 = 0 + 10.33333333 -13.83333333x + x2 = 0 + 10.33333333 Combine like terms: 0 + 10.33333333 = 10.33333333 -13.83333333x + x2 = 10.33333333 The x term is -13.83333333x. Take half its coefficient (-6.916666665). Square it (47.84027775) and add it to both sides. Add '47.84027775' to each side of the equation. -13.83333333x + 47.84027775 + x2 = 10.33333333 + 47.84027775 Reorder the terms: 47.84027775 + -13.83333333x + x2 = 10.33333333 + 47.84027775 Combine like terms: 10.33333333 + 47.84027775 = 58.17361108 47.84027775 + -13.83333333x + x2 = 58.17361108 Factor a perfect square on the left side: (x + -6.916666665)(x + -6.916666665) = 58.17361108 Calculate the square root of the right side: 7.627162715 Break this problem into two subproblems by setting (x + -6.916666665) equal to 7.627162715 and -7.627162715.Subproblem 1
x + -6.916666665 = 7.627162715 Simplifying x + -6.916666665 = 7.627162715 Reorder the terms: -6.916666665 + x = 7.627162715 Solving -6.916666665 + x = 7.627162715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.916666665' to each side of the equation. -6.916666665 + 6.916666665 + x = 7.627162715 + 6.916666665 Combine like terms: -6.916666665 + 6.916666665 = 0.000000000 0.000000000 + x = 7.627162715 + 6.916666665 x = 7.627162715 + 6.916666665 Combine like terms: 7.627162715 + 6.916666665 = 14.54382938 x = 14.54382938 Simplifying x = 14.54382938Subproblem 2
x + -6.916666665 = -7.627162715 Simplifying x + -6.916666665 = -7.627162715 Reorder the terms: -6.916666665 + x = -7.627162715 Solving -6.916666665 + x = -7.627162715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.916666665' to each side of the equation. -6.916666665 + 6.916666665 + x = -7.627162715 + 6.916666665 Combine like terms: -6.916666665 + 6.916666665 = 0.000000000 0.000000000 + x = -7.627162715 + 6.916666665 x = -7.627162715 + 6.916666665 Combine like terms: -7.627162715 + 6.916666665 = -0.71049605 x = -0.71049605 Simplifying x = -0.71049605Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.54382938, -0.71049605}
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