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Simplifying 4(0.25x2 + -20x + 15) = 0 Reorder the terms: 4(15 + -20x + 0.25x2) = 0 (15 * 4 + -20x * 4 + 0.25x2 * 4) = 0 (60 + -80x + 1x2) = 0 Solving 60 + -80x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -80x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -80x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -80x + x2 = 0 + -60 -80x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -80x + x2 = -60 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = -60 + 1600 Reorder the terms: 1600 + -80x + x2 = -60 + 1600 Combine like terms: -60 + 1600 = 1540 1600 + -80x + x2 = 1540 Factor a perfect square on the left side: (x + -40)(x + -40) = 1540 Calculate the square root of the right side: 39.242833741 Break this problem into two subproblems by setting (x + -40) equal to 39.242833741 and -39.242833741.Subproblem 1
x + -40 = 39.242833741 Simplifying x + -40 = 39.242833741 Reorder the terms: -40 + x = 39.242833741 Solving -40 + x = 39.242833741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 39.242833741 + 40 Combine like terms: -40 + 40 = 0 0 + x = 39.242833741 + 40 x = 39.242833741 + 40 Combine like terms: 39.242833741 + 40 = 79.242833741 x = 79.242833741 Simplifying x = 79.242833741Subproblem 2
x + -40 = -39.242833741 Simplifying x + -40 = -39.242833741 Reorder the terms: -40 + x = -39.242833741 Solving -40 + x = -39.242833741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -39.242833741 + 40 Combine like terms: -40 + 40 = 0 0 + x = -39.242833741 + 40 x = -39.242833741 + 40 Combine like terms: -39.242833741 + 40 = 0.757166259 x = 0.757166259 Simplifying x = 0.757166259Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.242833741, 0.757166259}
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