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Simplifying 1750 = x(x + 3) Reorder the terms: 1750 = x(3 + x) 1750 = (3 * x + x * x) 1750 = (3x + x2) Solving 1750 = 3x + x2 Solving for variable 'x'. Reorder the terms: 1750 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 1750 + -3x + -1x2 = 0 + x2 + -1x2 1750 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1750 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1750 + 3x + x2 = 0 Move the constant term to the right: Add '1750' to each side of the equation. -1750 + 3x + 1750 + x2 = 0 + 1750 Reorder the terms: -1750 + 1750 + 3x + x2 = 0 + 1750 Combine like terms: -1750 + 1750 = 0 0 + 3x + x2 = 0 + 1750 3x + x2 = 0 + 1750 Combine like terms: 0 + 1750 = 1750 3x + x2 = 1750 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 1750 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1750 + 2.25 Combine like terms: 1750 + 2.25 = 1752.25 2.25 + 3x + x2 = 1752.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1752.25 Calculate the square root of the right side: 41.859885332 Break this problem into two subproblems by setting (x + 1.5) equal to 41.859885332 and -41.859885332.Subproblem 1
x + 1.5 = 41.859885332 Simplifying x + 1.5 = 41.859885332 Reorder the terms: 1.5 + x = 41.859885332 Solving 1.5 + x = 41.859885332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 41.859885332 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 41.859885332 + -1.5 x = 41.859885332 + -1.5 Combine like terms: 41.859885332 + -1.5 = 40.359885332 x = 40.359885332 Simplifying x = 40.359885332Subproblem 2
x + 1.5 = -41.859885332 Simplifying x + 1.5 = -41.859885332 Reorder the terms: 1.5 + x = -41.859885332 Solving 1.5 + x = -41.859885332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -41.859885332 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -41.859885332 + -1.5 x = -41.859885332 + -1.5 Combine like terms: -41.859885332 + -1.5 = -43.359885332 x = -43.359885332 Simplifying x = -43.359885332Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.359885332, -43.359885332}
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