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Simplifying 7x(4x + 2) = 5 Reorder the terms: 7x(2 + 4x) = 5 (2 * 7x + 4x * 7x) = 5 (14x + 28x2) = 5 Solving 14x + 28x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 14x + 28x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 14x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.1785714286 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.5x + 0.1785714286 + x2 = 0 + 0.1785714286 Reorder the terms: -0.1785714286 + 0.1785714286 + 0.5x + x2 = 0 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + 0.1785714286 0.5x + x2 = 0 + 0.1785714286 Combine like terms: 0 + 0.1785714286 = 0.1785714286 0.5x + x2 = 0.1785714286 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.1785714286 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.1785714286 + 0.0625 Combine like terms: 0.1785714286 + 0.0625 = 0.2410714286 0.0625 + 0.5x + x2 = 0.2410714286 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.2410714286 Calculate the square root of the right side: 0.490990253 Break this problem into two subproblems by setting (x + 0.25) equal to 0.490990253 and -0.490990253.Subproblem 1
x + 0.25 = 0.490990253 Simplifying x + 0.25 = 0.490990253 Reorder the terms: 0.25 + x = 0.490990253 Solving 0.25 + x = 0.490990253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.490990253 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.490990253 + -0.25 x = 0.490990253 + -0.25 Combine like terms: 0.490990253 + -0.25 = 0.240990253 x = 0.240990253 Simplifying x = 0.240990253Subproblem 2
x + 0.25 = -0.490990253 Simplifying x + 0.25 = -0.490990253 Reorder the terms: 0.25 + x = -0.490990253 Solving 0.25 + x = -0.490990253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.490990253 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.490990253 + -0.25 x = -0.490990253 + -0.25 Combine like terms: -0.490990253 + -0.25 = -0.740990253 x = -0.740990253 Simplifying x = -0.740990253Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.240990253, -0.740990253}
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