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Simplifying 7x(4x + 3) = 5 Reorder the terms: 7x(3 + 4x) = 5 (3 * 7x + 4x * 7x) = 5 (21x + 28x2) = 5 Solving 21x + 28x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 21x + 28x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 21x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.1785714286 + 0.75x + x2 = 0 Move the constant term to the right: Add '0.1785714286' to each side of the equation. -0.1785714286 + 0.75x + 0.1785714286 + x2 = 0 + 0.1785714286 Reorder the terms: -0.1785714286 + 0.1785714286 + 0.75x + x2 = 0 + 0.1785714286 Combine like terms: -0.1785714286 + 0.1785714286 = 0.0000000000 0.0000000000 + 0.75x + x2 = 0 + 0.1785714286 0.75x + x2 = 0 + 0.1785714286 Combine like terms: 0 + 0.1785714286 = 0.1785714286 0.75x + x2 = 0.1785714286 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 0.1785714286 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 0.1785714286 + 0.140625 Combine like terms: 0.1785714286 + 0.140625 = 0.3191964286 0.140625 + 0.75x + x2 = 0.3191964286 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 0.3191964286 Calculate the square root of the right side: 0.564974715 Break this problem into two subproblems by setting (x + 0.375) equal to 0.564974715 and -0.564974715.Subproblem 1
x + 0.375 = 0.564974715 Simplifying x + 0.375 = 0.564974715 Reorder the terms: 0.375 + x = 0.564974715 Solving 0.375 + x = 0.564974715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 0.564974715 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 0.564974715 + -0.375 x = 0.564974715 + -0.375 Combine like terms: 0.564974715 + -0.375 = 0.189974715 x = 0.189974715 Simplifying x = 0.189974715Subproblem 2
x + 0.375 = -0.564974715 Simplifying x + 0.375 = -0.564974715 Reorder the terms: 0.375 + x = -0.564974715 Solving 0.375 + x = -0.564974715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -0.564974715 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -0.564974715 + -0.375 x = -0.564974715 + -0.375 Combine like terms: -0.564974715 + -0.375 = -0.939974715 x = -0.939974715 Simplifying x = -0.939974715Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.189974715, -0.939974715}
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