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Simplifying (7x + 7)(4x) = 5 Reorder the terms: (7 + 7x)(4x) = 5 Remove parenthesis around (4x) (7 + 7x) * 4x = 5 Reorder the terms for easier multiplication: 4x(7 + 7x) = 5 (7 * 4x + 7x * 4x) = 5 (28x + 28x2) = 5 Solving 28x + 28x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 28x + 28x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 28x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.1785714286 + x + x2 = 0 Move the constant term to the right: Add '0.1785714286' to each side of the equation. -0.1785714286 + x + 0.1785714286 + x2 = 0 + 0.1785714286 Reorder the terms: -0.1785714286 + 0.1785714286 + x + x2 = 0 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + x + x2 = 0 + 0.1785714286 x + x2 = 0 + 0.1785714286 Combine like terms: 0 + 0.1785714286 = 0.1785714286 x + x2 = 0.1785714286 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.1785714286 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.1785714286 + 0.25 Combine like terms: 0.1785714286 + 0.25 = 0.4285714286 1.25 + x2 = 0.4285714286 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.4285714286 Calculate the square root of the right side: 0.654653671 Break this problem into two subproblems by setting (x + 0.5) equal to 0.654653671 and -0.654653671.Subproblem 1
x + 0.5 = 0.654653671 Simplifying x + 0.5 = 0.654653671 Reorder the terms: 0.5 + x = 0.654653671 Solving 0.5 + x = 0.654653671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.654653671 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.654653671 + -0.5 x = 0.654653671 + -0.5 Combine like terms: 0.654653671 + -0.5 = 0.154653671 x = 0.154653671 Simplifying x = 0.154653671Subproblem 2
x + 0.5 = -0.654653671 Simplifying x + 0.5 = -0.654653671 Reorder the terms: 0.5 + x = -0.654653671 Solving 0.5 + x = -0.654653671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.654653671 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.654653671 + -0.5 x = -0.654653671 + -0.5 Combine like terms: -0.654653671 + -0.5 = -1.154653671 x = -1.154653671 Simplifying x = -1.154653671Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.154653671, -1.154653671}
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