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Simplifying 5(x + 2) * 7x = 23 Reorder the terms: 5(2 + x) * 7x = 23 Reorder the terms for easier multiplication: 5 * 7x(2 + x) = 23 Multiply 5 * 7 35x(2 + x) = 23 (2 * 35x + x * 35x) = 23 (70x + 35x2) = 23 Solving 70x + 35x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + 70x + 35x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 70x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.6571428571 + 2x + x2 = 0 Move the constant term to the right: Add '0.6571428571' to each side of the equation. -0.6571428571 + 2x + 0.6571428571 + x2 = 0 + 0.6571428571 Reorder the terms: -0.6571428571 + 0.6571428571 + 2x + x2 = 0 + 0.6571428571 Combine like terms: -0.6571428571 + 0.6571428571 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + 0.6571428571 2x + x2 = 0 + 0.6571428571 Combine like terms: 0 + 0.6571428571 = 0.6571428571 2x + x2 = 0.6571428571 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.6571428571 + 1 Reorder the terms: 1 + 2x + x2 = 0.6571428571 + 1 Combine like terms: 0.6571428571 + 1 = 1.6571428571 1 + 2x + x2 = 1.6571428571 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.6571428571 Calculate the square root of the right side: 1.287300609 Break this problem into two subproblems by setting (x + 1) equal to 1.287300609 and -1.287300609.Subproblem 1
x + 1 = 1.287300609 Simplifying x + 1 = 1.287300609 Reorder the terms: 1 + x = 1.287300609 Solving 1 + x = 1.287300609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.287300609 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.287300609 + -1 x = 1.287300609 + -1 Combine like terms: 1.287300609 + -1 = 0.287300609 x = 0.287300609 Simplifying x = 0.287300609Subproblem 2
x + 1 = -1.287300609 Simplifying x + 1 = -1.287300609 Reorder the terms: 1 + x = -1.287300609 Solving 1 + x = -1.287300609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.287300609 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.287300609 + -1 x = -1.287300609 + -1 Combine like terms: -1.287300609 + -1 = -2.287300609 x = -2.287300609 Simplifying x = -2.287300609Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.287300609, -2.287300609}
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