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Simplifying 0.25 = (30 + -1x) * x Reorder the terms for easier multiplication: 0.25 = x(30 + -1x) 0.25 = (30 * x + -1x * x) 0.25 = (30x + -1x2) Solving 0.25 = 30x + -1x2 Solving for variable 'x'. Reorder the terms: 0.25 + -30x + x2 = 30x + -30x + -1x2 + x2 Combine like terms: 30x + -30x = 0 0.25 + -30x + x2 = 0 + -1x2 + x2 0.25 + -30x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 0.25 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -30x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -30x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -30x + x2 = 0 + -0.25 -30x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -30x + x2 = -0.25 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -0.25 + 225 Reorder the terms: 225 + -30x + x2 = -0.25 + 225 Combine like terms: -0.25 + 225 = 224.75 225 + -30x + x2 = 224.75 Factor a perfect square on the left side: (x + -15)(x + -15) = 224.75 Calculate the square root of the right side: 14.991664351 Break this problem into two subproblems by setting (x + -15) equal to 14.991664351 and -14.991664351.Subproblem 1
x + -15 = 14.991664351 Simplifying x + -15 = 14.991664351 Reorder the terms: -15 + x = 14.991664351 Solving -15 + x = 14.991664351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 14.991664351 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.991664351 + 15 x = 14.991664351 + 15 Combine like terms: 14.991664351 + 15 = 29.991664351 x = 29.991664351 Simplifying x = 29.991664351Subproblem 2
x + -15 = -14.991664351 Simplifying x + -15 = -14.991664351 Reorder the terms: -15 + x = -14.991664351 Solving -15 + x = -14.991664351 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -14.991664351 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.991664351 + 15 x = -14.991664351 + 15 Combine like terms: -14.991664351 + 15 = 0.008335649 x = 0.008335649 Simplifying x = 0.008335649Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.991664351, 0.008335649}
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