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Simplifying 5x(4x + 5) = 3 Reorder the terms: 5x(5 + 4x) = 3 (5 * 5x + 4x * 5x) = 3 (25x + 20x2) = 3 Solving 25x + 20x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 25x + 20x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 25x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.15 + 1.25x + x2 = 0.0 Move the constant term to the right: Add '0.15' to each side of the equation. -0.15 + 1.25x + 0.15 + x2 = 0.0 + 0.15 Reorder the terms: -0.15 + 0.15 + 1.25x + x2 = 0.0 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + 1.25x + x2 = 0.0 + 0.15 1.25x + x2 = 0.0 + 0.15 Combine like terms: 0.0 + 0.15 = 0.15 1.25x + x2 = 0.15 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 0.15 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 0.15 + 0.390625 Combine like terms: 0.15 + 0.390625 = 0.540625 0.390625 + 1.25x + x2 = 0.540625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 0.540625 Calculate the square root of the right side: 0.735272058 Break this problem into two subproblems by setting (x + 0.625) equal to 0.735272058 and -0.735272058.Subproblem 1
x + 0.625 = 0.735272058 Simplifying x + 0.625 = 0.735272058 Reorder the terms: 0.625 + x = 0.735272058 Solving 0.625 + x = 0.735272058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 0.735272058 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 0.735272058 + -0.625 x = 0.735272058 + -0.625 Combine like terms: 0.735272058 + -0.625 = 0.110272058 x = 0.110272058 Simplifying x = 0.110272058Subproblem 2
x + 0.625 = -0.735272058 Simplifying x + 0.625 = -0.735272058 Reorder the terms: 0.625 + x = -0.735272058 Solving 0.625 + x = -0.735272058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -0.735272058 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -0.735272058 + -0.625 x = -0.735272058 + -0.625 Combine like terms: -0.735272058 + -0.625 = -1.360272058 x = -1.360272058 Simplifying x = -1.360272058Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.110272058, -1.360272058}
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