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Simplifying 5.8(0.12 + -0.7x + x2) = x (0.12 * 5.8 + -0.7x * 5.8 + x2 * 5.8) = x (0.696 + -4.06x + 5.8x2) = x Solving 0.696 + -4.06x + 5.8x2 = x Solving for variable 'x'. Reorder the terms: 0.696 + -4.06x + -1x + 5.8x2 = x + -1x Combine like terms: -4.06x + -1x = -5.06x 0.696 + -5.06x + 5.8x2 = x + -1x Combine like terms: x + -1x = 0 0.696 + -5.06x + 5.8x2 = 0 Begin completing the square. Divide all terms by 5.8 the coefficient of the squared term: Divide each side by '5.8'. 0.12 + -0.8724137931x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -0.8724137931x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -0.8724137931x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -0.8724137931x + x2 = 0 + -0.12 -0.8724137931x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -0.8724137931x + x2 = -0.12 The x term is -0.8724137931x. Take half its coefficient (-0.4362068966). Square it (0.1902764566) and add it to both sides. Add '0.1902764566' to each side of the equation. -0.8724137931x + 0.1902764566 + x2 = -0.12 + 0.1902764566 Reorder the terms: 0.1902764566 + -0.8724137931x + x2 = -0.12 + 0.1902764566 Combine like terms: -0.12 + 0.1902764566 = 0.0702764566 0.1902764566 + -0.8724137931x + x2 = 0.0702764566 Factor a perfect square on the left side: (x + -0.4362068966)(x + -0.4362068966) = 0.0702764566 Calculate the square root of the right side: 0.26509707 Break this problem into two subproblems by setting (x + -0.4362068966) equal to 0.26509707 and -0.26509707.Subproblem 1
x + -0.4362068966 = 0.26509707 Simplifying x + -0.4362068966 = 0.26509707 Reorder the terms: -0.4362068966 + x = 0.26509707 Solving -0.4362068966 + x = 0.26509707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4362068966' to each side of the equation. -0.4362068966 + 0.4362068966 + x = 0.26509707 + 0.4362068966 Combine like terms: -0.4362068966 + 0.4362068966 = 0.0000000000 0.0000000000 + x = 0.26509707 + 0.4362068966 x = 0.26509707 + 0.4362068966 Combine like terms: 0.26509707 + 0.4362068966 = 0.7013039666 x = 0.7013039666 Simplifying x = 0.7013039666Subproblem 2
x + -0.4362068966 = -0.26509707 Simplifying x + -0.4362068966 = -0.26509707 Reorder the terms: -0.4362068966 + x = -0.26509707 Solving -0.4362068966 + x = -0.26509707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4362068966' to each side of the equation. -0.4362068966 + 0.4362068966 + x = -0.26509707 + 0.4362068966 Combine like terms: -0.4362068966 + 0.4362068966 = 0.0000000000 0.0000000000 + x = -0.26509707 + 0.4362068966 x = -0.26509707 + 0.4362068966 Combine like terms: -0.26509707 + 0.4362068966 = 0.1711098266 x = 0.1711098266 Simplifying x = 0.1711098266Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7013039666, 0.1711098266}
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