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Simplifying 0 = -0.01x2 + 0.25x + 9.04 Reorder the terms: 0 = 9.04 + 0.25x + -0.01x2 Solving 0 = 9.04 + 0.25x + -0.01x2 Solving for variable 'x'. Combine like terms: 0 + -9.04 = -9.04 -9.04 + -0.25x + 0.01x2 = 9.04 + 0.25x + -0.01x2 + -9.04 + -0.25x + 0.01x2 Reorder the terms: -9.04 + -0.25x + 0.01x2 = 9.04 + -9.04 + 0.25x + -0.25x + -0.01x2 + 0.01x2 Combine like terms: 9.04 + -9.04 = 0.00 -9.04 + -0.25x + 0.01x2 = 0.00 + 0.25x + -0.25x + -0.01x2 + 0.01x2 -9.04 + -0.25x + 0.01x2 = 0.25x + -0.25x + -0.01x2 + 0.01x2 Combine like terms: 0.25x + -0.25x = 0.00 -9.04 + -0.25x + 0.01x2 = 0.00 + -0.01x2 + 0.01x2 -9.04 + -0.25x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 -9.04 + -0.25x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -904 + -25x + x2 = 0 Move the constant term to the right: Add '904' to each side of the equation. -904 + -25x + 904 + x2 = 0 + 904 Reorder the terms: -904 + 904 + -25x + x2 = 0 + 904 Combine like terms: -904 + 904 = 0 0 + -25x + x2 = 0 + 904 -25x + x2 = 0 + 904 Combine like terms: 0 + 904 = 904 -25x + x2 = 904 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = 904 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 904 + 156.25 Combine like terms: 904 + 156.25 = 1060.25 156.25 + -25x + x2 = 1060.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 1060.25 Calculate the square root of the right side: 32.56148031 Break this problem into two subproblems by setting (x + -12.5) equal to 32.56148031 and -32.56148031.Subproblem 1
x + -12.5 = 32.56148031 Simplifying x + -12.5 = 32.56148031 Reorder the terms: -12.5 + x = 32.56148031 Solving -12.5 + x = 32.56148031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 32.56148031 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 32.56148031 + 12.5 x = 32.56148031 + 12.5 Combine like terms: 32.56148031 + 12.5 = 45.06148031 x = 45.06148031 Simplifying x = 45.06148031Subproblem 2
x + -12.5 = -32.56148031 Simplifying x + -12.5 = -32.56148031 Reorder the terms: -12.5 + x = -32.56148031 Solving -12.5 + x = -32.56148031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -32.56148031 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -32.56148031 + 12.5 x = -32.56148031 + 12.5 Combine like terms: -32.56148031 + 12.5 = -20.06148031 x = -20.06148031 Simplifying x = -20.06148031Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.06148031, -20.06148031}
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