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Simplifying 14 + 3(x + 10) = 7(2x + 4) * x Reorder the terms: 14 + 3(10 + x) = 7(2x + 4) * x 14 + (10 * 3 + x * 3) = 7(2x + 4) * x 14 + (30 + 3x) = 7(2x + 4) * x Combine like terms: 14 + 30 = 44 44 + 3x = 7(2x + 4) * x Reorder the terms: 44 + 3x = 7(4 + 2x) * x Reorder the terms for easier multiplication: 44 + 3x = 7x(4 + 2x) 44 + 3x = (4 * 7x + 2x * 7x) 44 + 3x = (28x + 14x2) Solving 44 + 3x = 28x + 14x2 Solving for variable 'x'. Combine like terms: 3x + -28x = -25x 44 + -25x + -14x2 = 28x + 14x2 + -28x + -14x2 Reorder the terms: 44 + -25x + -14x2 = 28x + -28x + 14x2 + -14x2 Combine like terms: 28x + -28x = 0 44 + -25x + -14x2 = 0 + 14x2 + -14x2 44 + -25x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 44 + -25x + -14x2 = 0 Begin completing the square. Divide all terms by -14 the coefficient of the squared term: Divide each side by '-14'. -3.142857143 + 1.785714286x + x2 = 0 Move the constant term to the right: Add '3.142857143' to each side of the equation. -3.142857143 + 1.785714286x + 3.142857143 + x2 = 0 + 3.142857143 Reorder the terms: -3.142857143 + 3.142857143 + 1.785714286x + x2 = 0 + 3.142857143 Combine like terms: -3.142857143 + 3.142857143 = 0.000000000 0.000000000 + 1.785714286x + x2 = 0 + 3.142857143 1.785714286x + x2 = 0 + 3.142857143 Combine like terms: 0 + 3.142857143 = 3.142857143 1.785714286x + x2 = 3.142857143 The x term is 1.785714286x. Take half its coefficient (0.892857143). Square it (0.7971938778) and add it to both sides. Add '0.7971938778' to each side of the equation. 1.785714286x + 0.7971938778 + x2 = 3.142857143 + 0.7971938778 Reorder the terms: 0.7971938778 + 1.785714286x + x2 = 3.142857143 + 0.7971938778 Combine like terms: 3.142857143 + 0.7971938778 = 3.9400510208 0.7971938778 + 1.785714286x + x2 = 3.9400510208 Factor a perfect square on the left side: (x + 0.892857143)(x + 0.892857143) = 3.9400510208 Calculate the square root of the right side: 1.984956176 Break this problem into two subproblems by setting (x + 0.892857143) equal to 1.984956176 and -1.984956176.Subproblem 1
x + 0.892857143 = 1.984956176 Simplifying x + 0.892857143 = 1.984956176 Reorder the terms: 0.892857143 + x = 1.984956176 Solving 0.892857143 + x = 1.984956176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.892857143' to each side of the equation. 0.892857143 + -0.892857143 + x = 1.984956176 + -0.892857143 Combine like terms: 0.892857143 + -0.892857143 = 0.000000000 0.000000000 + x = 1.984956176 + -0.892857143 x = 1.984956176 + -0.892857143 Combine like terms: 1.984956176 + -0.892857143 = 1.092099033 x = 1.092099033 Simplifying x = 1.092099033Subproblem 2
x + 0.892857143 = -1.984956176 Simplifying x + 0.892857143 = -1.984956176 Reorder the terms: 0.892857143 + x = -1.984956176 Solving 0.892857143 + x = -1.984956176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.892857143' to each side of the equation. 0.892857143 + -0.892857143 + x = -1.984956176 + -0.892857143 Combine like terms: 0.892857143 + -0.892857143 = 0.000000000 0.000000000 + x = -1.984956176 + -0.892857143 x = -1.984956176 + -0.892857143 Combine like terms: -1.984956176 + -0.892857143 = -2.877813319 x = -2.877813319 Simplifying x = -2.877813319Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.092099033, -2.877813319}
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