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Simplifying x + -1([29 + -2x](76x + -45)) = 3x + -342 Reorder the terms: x + -1([29 + -2x](-45 + 76x)) = 3x + -342 Multiply [29 + -2x] * (-45 + 76x) x + -1([29(-45 + 76x) + -2x * (-45 + 76x)]) = 3x + -342 x + -1([(-45 * 29 + 76x * 29) + -2x * (-45 + 76x)]) = 3x + -342 x + -1([(-1305 + 2204x) + -2x * (-45 + 76x)]) = 3x + -342 x + -1([-1305 + 2204x + (-45 * -2x + 76x * -2x)]) = 3x + -342 x + -1([-1305 + 2204x + (90x + -152x2)]) = 3x + -342 Combine like terms: 2204x + 90x = 2294x x + -1([-1305 + 2294x + -152x2]) = 3x + -342 x + (-1305 * -1 + 2294x * -1 + -152x2 * -1) = 3x + -342 x + (1305 + -2294x + 152x2) = 3x + -342 Reorder the terms: 1305 + x + -2294x + 152x2 = 3x + -342 Combine like terms: x + -2294x = -2293x 1305 + -2293x + 152x2 = 3x + -342 Reorder the terms: 1305 + -2293x + 152x2 = -342 + 3x Solving 1305 + -2293x + 152x2 = -342 + 3x Solving for variable 'x'. Reorder the terms: 1305 + 342 + -2293x + -3x + 152x2 = -342 + 3x + 342 + -3x Combine like terms: 1305 + 342 = 1647 1647 + -2293x + -3x + 152x2 = -342 + 3x + 342 + -3x Combine like terms: -2293x + -3x = -2296x 1647 + -2296x + 152x2 = -342 + 3x + 342 + -3x Reorder the terms: 1647 + -2296x + 152x2 = -342 + 342 + 3x + -3x Combine like terms: -342 + 342 = 0 1647 + -2296x + 152x2 = 0 + 3x + -3x 1647 + -2296x + 152x2 = 3x + -3x Combine like terms: 3x + -3x = 0 1647 + -2296x + 152x2 = 0 Begin completing the square. Divide all terms by 152 the coefficient of the squared term: Divide each side by '152'. 10.83552632 + -15.10526316x + x2 = 0 Move the constant term to the right: Add '-10.83552632' to each side of the equation. 10.83552632 + -15.10526316x + -10.83552632 + x2 = 0 + -10.83552632 Reorder the terms: 10.83552632 + -10.83552632 + -15.10526316x + x2 = 0 + -10.83552632 Combine like terms: 10.83552632 + -10.83552632 = 0.00000000 0.00000000 + -15.10526316x + x2 = 0 + -10.83552632 -15.10526316x + x2 = 0 + -10.83552632 Combine like terms: 0 + -10.83552632 = -10.83552632 -15.10526316x + x2 = -10.83552632 The x term is -15.10526316x. Take half its coefficient (-7.55263158). Square it (57.04224378) and add it to both sides. Add '57.04224378' to each side of the equation. -15.10526316x + 57.04224378 + x2 = -10.83552632 + 57.04224378 Reorder the terms: 57.04224378 + -15.10526316x + x2 = -10.83552632 + 57.04224378 Combine like terms: -10.83552632 + 57.04224378 = 46.20671746 57.04224378 + -15.10526316x + x2 = 46.20671746 Factor a perfect square on the left side: (x + -7.55263158)(x + -7.55263158) = 46.20671746 Calculate the square root of the right side: 6.797552314 Break this problem into two subproblems by setting (x + -7.55263158) equal to 6.797552314 and -6.797552314.Subproblem 1
x + -7.55263158 = 6.797552314 Simplifying x + -7.55263158 = 6.797552314 Reorder the terms: -7.55263158 + x = 6.797552314 Solving -7.55263158 + x = 6.797552314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.55263158' to each side of the equation. -7.55263158 + 7.55263158 + x = 6.797552314 + 7.55263158 Combine like terms: -7.55263158 + 7.55263158 = 0.00000000 0.00000000 + x = 6.797552314 + 7.55263158 x = 6.797552314 + 7.55263158 Combine like terms: 6.797552314 + 7.55263158 = 14.350183894 x = 14.350183894 Simplifying x = 14.350183894Subproblem 2
x + -7.55263158 = -6.797552314 Simplifying x + -7.55263158 = -6.797552314 Reorder the terms: -7.55263158 + x = -6.797552314 Solving -7.55263158 + x = -6.797552314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.55263158' to each side of the equation. -7.55263158 + 7.55263158 + x = -6.797552314 + 7.55263158 Combine like terms: -7.55263158 + 7.55263158 = 0.00000000 0.00000000 + x = -6.797552314 + 7.55263158 x = -6.797552314 + 7.55263158 Combine like terms: -6.797552314 + 7.55263158 = 0.755079266 x = 0.755079266 Simplifying x = 0.755079266Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.350183894, 0.755079266}
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