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Simplifying 4x(2x + 5) = 15 Reorder the terms: 4x(5 + 2x) = 15 (5 * 4x + 2x * 4x) = 15 (20x + 8x2) = 15 Solving 20x + 8x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 20x + 8x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + 2.5x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 2.5x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 2.5x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 2.5x + x2 = 0 + 1.875 2.5x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 2.5x + x2 = 1.875 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 1.875 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 1.875 + 1.5625 Combine like terms: 1.875 + 1.5625 = 3.4375 1.5625 + 2.5x + x2 = 3.4375 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 3.4375 Calculate the square root of the right side: 1.854049622 Break this problem into two subproblems by setting (x + 1.25) equal to 1.854049622 and -1.854049622.Subproblem 1
x + 1.25 = 1.854049622 Simplifying x + 1.25 = 1.854049622 Reorder the terms: 1.25 + x = 1.854049622 Solving 1.25 + x = 1.854049622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.854049622 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.854049622 + -1.25 x = 1.854049622 + -1.25 Combine like terms: 1.854049622 + -1.25 = 0.604049622 x = 0.604049622 Simplifying x = 0.604049622Subproblem 2
x + 1.25 = -1.854049622 Simplifying x + 1.25 = -1.854049622 Reorder the terms: 1.25 + x = -1.854049622 Solving 1.25 + x = -1.854049622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.854049622 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.854049622 + -1.25 x = -1.854049622 + -1.25 Combine like terms: -1.854049622 + -1.25 = -3.104049622 x = -3.104049622 Simplifying x = -3.104049622Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.604049622, -3.104049622}
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