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Simplifying 5(x + 2) * 7x + 4 = 0 Reorder the terms: 5(2 + x) * 7x + 4 = 0 Reorder the terms for easier multiplication: 5 * 7x(2 + x) + 4 = 0 Multiply 5 * 7 35x(2 + x) + 4 = 0 (2 * 35x + x * 35x) + 4 = 0 (70x + 35x2) + 4 = 0 Reorder the terms: 4 + 70x + 35x2 = 0 Solving 4 + 70x + 35x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 0.1142857143 + 2x + x2 = 0 Move the constant term to the right: Add '-0.1142857143' to each side of the equation. 0.1142857143 + 2x + -0.1142857143 + x2 = 0 + -0.1142857143 Reorder the terms: 0.1142857143 + -0.1142857143 + 2x + x2 = 0 + -0.1142857143 Combine like terms: 0.1142857143 + -0.1142857143 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + -0.1142857143 2x + x2 = 0 + -0.1142857143 Combine like terms: 0 + -0.1142857143 = -0.1142857143 2x + x2 = -0.1142857143 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 = -0.1142857143 + 1 Reorder the terms: 1 + 2x + x2 = -0.1142857143 + 1 Combine like terms: -0.1142857143 + 1 = 0.8857142857 1 + 2x + x2 = 0.8857142857 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.8857142857 Calculate the square root of the right side: 0.941123948 Break this problem into two subproblems by setting (x + 1) equal to 0.941123948 and -0.941123948.Subproblem 1
x + 1 = 0.941123948 Simplifying x + 1 = 0.941123948 Reorder the terms: 1 + x = 0.941123948 Solving 1 + x = 0.941123948 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 = 0.941123948 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.941123948 + -1 x = 0.941123948 + -1 Combine like terms: 0.941123948 + -1 = -0.058876052 x = -0.058876052 Simplifying x = -0.058876052Subproblem 2
x + 1 = -0.941123948 Simplifying x + 1 = -0.941123948 Reorder the terms: 1 + x = -0.941123948 Solving 1 + x = -0.941123948 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 = -0.941123948 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.941123948 + -1 x = -0.941123948 + -1 Combine like terms: -0.941123948 + -1 = -1.941123948 x = -1.941123948 Simplifying x = -1.941123948Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.058876052, -1.941123948}
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