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Simplifying 0 = -32x2 + 2025x + 364500 Reorder the terms: 0 = 364500 + 2025x + -32x2 Solving 0 = 364500 + 2025x + -32x2 Solving for variable 'x'. Combine like terms: 0 + -364500 = -364500 -364500 + -2025x + 32x2 = 364500 + 2025x + -32x2 + -364500 + -2025x + 32x2 Reorder the terms: -364500 + -2025x + 32x2 = 364500 + -364500 + 2025x + -2025x + -32x2 + 32x2 Combine like terms: 364500 + -364500 = 0 -364500 + -2025x + 32x2 = 0 + 2025x + -2025x + -32x2 + 32x2 -364500 + -2025x + 32x2 = 2025x + -2025x + -32x2 + 32x2 Combine like terms: 2025x + -2025x = 0 -364500 + -2025x + 32x2 = 0 + -32x2 + 32x2 -364500 + -2025x + 32x2 = -32x2 + 32x2 Combine like terms: -32x2 + 32x2 = 0 -364500 + -2025x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -11390.625 + -63.28125x + x2 = 0 Move the constant term to the right: Add '11390.625' to each side of the equation. -11390.625 + -63.28125x + 11390.625 + x2 = 0 + 11390.625 Reorder the terms: -11390.625 + 11390.625 + -63.28125x + x2 = 0 + 11390.625 Combine like terms: -11390.625 + 11390.625 = 0.000 0.000 + -63.28125x + x2 = 0 + 11390.625 -63.28125x + x2 = 0 + 11390.625 Combine like terms: 0 + 11390.625 = 11390.625 -63.28125x + x2 = 11390.625 The x term is -63.28125x. Take half its coefficient (-31.640625). Square it (1001.129150) and add it to both sides. Add '1001.129150' to each side of the equation. -63.28125x + 1001.129150 + x2 = 11390.625 + 1001.129150 Reorder the terms: 1001.129150 + -63.28125x + x2 = 11390.625 + 1001.129150 Combine like terms: 11390.625 + 1001.129150 = 12391.75415 1001.129150 + -63.28125x + x2 = 12391.75415 Factor a perfect square on the left side: (x + -31.640625)(x + -31.640625) = 12391.75415 Calculate the square root of the right side: 111.31825614 Break this problem into two subproblems by setting (x + -31.640625) equal to 111.31825614 and -111.31825614.Subproblem 1
x + -31.640625 = 111.31825614 Simplifying x + -31.640625 = 111.31825614 Reorder the terms: -31.640625 + x = 111.31825614 Solving -31.640625 + x = 111.31825614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.640625' to each side of the equation. -31.640625 + 31.640625 + x = 111.31825614 + 31.640625 Combine like terms: -31.640625 + 31.640625 = 0.000000 0.000000 + x = 111.31825614 + 31.640625 x = 111.31825614 + 31.640625 Combine like terms: 111.31825614 + 31.640625 = 142.95888114 x = 142.95888114 Simplifying x = 142.95888114Subproblem 2
x + -31.640625 = -111.31825614 Simplifying x + -31.640625 = -111.31825614 Reorder the terms: -31.640625 + x = -111.31825614 Solving -31.640625 + x = -111.31825614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '31.640625' to each side of the equation. -31.640625 + 31.640625 + x = -111.31825614 + 31.640625 Combine like terms: -31.640625 + 31.640625 = 0.000000 0.000000 + x = -111.31825614 + 31.640625 x = -111.31825614 + 31.640625 Combine like terms: -111.31825614 + 31.640625 = -79.67763114 x = -79.67763114 Simplifying x = -79.67763114Solution
The solution to the problem is based on the solutions from the subproblems. x = {142.95888114, -79.67763114}
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