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Simplifying 7x(4x + 1) = 5 Reorder the terms: 7x(1 + 4x) = 5 (1 * 7x + 4x * 7x) = 5 (7x + 28x2) = 5 Solving 7x + 28x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 7x + 28x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 7x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.1785714286 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.25x + 0.1785714286 + x2 = 0 + 0.1785714286 Reorder the terms: -0.1785714286 + 0.1785714286 + 0.25x + x2 = 0 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + 0.25x + x2 = 0 + 0.1785714286 0.25x + x2 = 0 + 0.1785714286 Combine like terms: 0 + 0.1785714286 = 0.1785714286 0.25x + x2 = 0.1785714286 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.1785714286 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.1785714286 + 0.015625 Combine like terms: 0.1785714286 + 0.015625 = 0.1941964286 0.015625 + 0.25x + x2 = 0.1941964286 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.1941964286 Calculate the square root of the right side: 0.440677239 Break this problem into two subproblems by setting (x + 0.125) equal to 0.440677239 and -0.440677239.Subproblem 1
x + 0.125 = 0.440677239 Simplifying x + 0.125 = 0.440677239 Reorder the terms: 0.125 + x = 0.440677239 Solving 0.125 + x = 0.440677239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.440677239 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.440677239 + -0.125 x = 0.440677239 + -0.125 Combine like terms: 0.440677239 + -0.125 = 0.315677239 x = 0.315677239 Simplifying x = 0.315677239Subproblem 2
x + 0.125 = -0.440677239 Simplifying x + 0.125 = -0.440677239 Reorder the terms: 0.125 + x = -0.440677239 Solving 0.125 + x = -0.440677239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.440677239 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.440677239 + -0.125 x = -0.440677239 + -0.125 Combine like terms: -0.440677239 + -0.125 = -0.565677239 x = -0.565677239 Simplifying x = -0.565677239Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.315677239, -0.565677239}
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