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Simplifying 5x(4x + 7) = 5 + -2x + 4 Reorder the terms: 5x(7 + 4x) = 5 + -2x + 4 (7 * 5x + 4x * 5x) = 5 + -2x + 4 (35x + 20x2) = 5 + -2x + 4 Reorder the terms: 35x + 20x2 = 5 + 4 + -2x Combine like terms: 5 + 4 = 9 35x + 20x2 = 9 + -2x Solving 35x + 20x2 = 9 + -2x Solving for variable 'x'. Reorder the terms: -9 + 35x + 2x + 20x2 = 9 + -2x + -9 + 2x Combine like terms: 35x + 2x = 37x -9 + 37x + 20x2 = 9 + -2x + -9 + 2x Reorder the terms: -9 + 37x + 20x2 = 9 + -9 + -2x + 2x Combine like terms: 9 + -9 = 0 -9 + 37x + 20x2 = 0 + -2x + 2x -9 + 37x + 20x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -9 + 37x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.45 + 1.85x + x2 = 0.0 Move the constant term to the right: Add '0.45' to each side of the equation. -0.45 + 1.85x + 0.45 + x2 = 0.0 + 0.45 Reorder the terms: -0.45 + 0.45 + 1.85x + x2 = 0.0 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + 1.85x + x2 = 0.0 + 0.45 1.85x + x2 = 0.0 + 0.45 Combine like terms: 0.0 + 0.45 = 0.45 1.85x + x2 = 0.45 The x term is 1.85x. Take half its coefficient (0.925). Square it (0.855625) and add it to both sides. Add '0.855625' to each side of the equation. 1.85x + 0.855625 + x2 = 0.45 + 0.855625 Reorder the terms: 0.855625 + 1.85x + x2 = 0.45 + 0.855625 Combine like terms: 0.45 + 0.855625 = 1.305625 0.855625 + 1.85x + x2 = 1.305625 Factor a perfect square on the left side: (x + 0.925)(x + 0.925) = 1.305625 Calculate the square root of the right side: 1.142639488 Break this problem into two subproblems by setting (x + 0.925) equal to 1.142639488 and -1.142639488.Subproblem 1
x + 0.925 = 1.142639488 Simplifying x + 0.925 = 1.142639488 Reorder the terms: 0.925 + x = 1.142639488 Solving 0.925 + x = 1.142639488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.925' to each side of the equation. 0.925 + -0.925 + x = 1.142639488 + -0.925 Combine like terms: 0.925 + -0.925 = 0.000 0.000 + x = 1.142639488 + -0.925 x = 1.142639488 + -0.925 Combine like terms: 1.142639488 + -0.925 = 0.217639488 x = 0.217639488 Simplifying x = 0.217639488Subproblem 2
x + 0.925 = -1.142639488 Simplifying x + 0.925 = -1.142639488 Reorder the terms: 0.925 + x = -1.142639488 Solving 0.925 + x = -1.142639488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.925' to each side of the equation. 0.925 + -0.925 + x = -1.142639488 + -0.925 Combine like terms: 0.925 + -0.925 = 0.000 0.000 + x = -1.142639488 + -0.925 x = -1.142639488 + -0.925 Combine like terms: -1.142639488 + -0.925 = -2.067639488 x = -2.067639488 Simplifying x = -2.067639488Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.217639488, -2.067639488}
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