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Simplifying 5x(4x + 3) = 66 Reorder the terms: 5x(3 + 4x) = 66 (3 * 5x + 4x * 5x) = 66 (15x + 20x2) = 66 Solving 15x + 20x2 = 66 Solving for variable 'x'. Reorder the terms: -66 + 15x + 20x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -66 + 15x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -3.3 + 0.75x + x2 = 0.0 Move the constant term to the right: Add '3.3' to each side of the equation. -3.3 + 0.75x + 3.3 + x2 = 0.0 + 3.3 Reorder the terms: -3.3 + 3.3 + 0.75x + x2 = 0.0 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + 0.75x + x2 = 0.0 + 3.3 0.75x + x2 = 0.0 + 3.3 Combine like terms: 0.0 + 3.3 = 3.3 0.75x + x2 = 3.3 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 = 3.3 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 3.3 + 0.140625 Combine like terms: 3.3 + 0.140625 = 3.440625 0.140625 + 0.75x + x2 = 3.440625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 3.440625 Calculate the square root of the right side: 1.85489218 Break this problem into two subproblems by setting (x + 0.375) equal to 1.85489218 and -1.85489218.Subproblem 1
x + 0.375 = 1.85489218 Simplifying x + 0.375 = 1.85489218 Reorder the terms: 0.375 + x = 1.85489218 Solving 0.375 + x = 1.85489218 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 = 1.85489218 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.85489218 + -0.375 x = 1.85489218 + -0.375 Combine like terms: 1.85489218 + -0.375 = 1.47989218 x = 1.47989218 Simplifying x = 1.47989218Subproblem 2
x + 0.375 = -1.85489218 Simplifying x + 0.375 = -1.85489218 Reorder the terms: 0.375 + x = -1.85489218 Solving 0.375 + x = -1.85489218 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 = -1.85489218 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.85489218 + -0.375 x = -1.85489218 + -0.375 Combine like terms: -1.85489218 + -0.375 = -2.22989218 x = -2.22989218 Simplifying x = -2.22989218Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.47989218, -2.22989218}
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