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Simplifying 1.5x2 + 15x = 1500 Reorder the terms: 15x + 1.5x2 = 1500 Solving 15x + 1.5x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + 15x + 1.5x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + 15x + 1.5x2 = 0 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -1000 + 10x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 10x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 10x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 10x + x2 = 0 + 1000 10x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 10x + x2 = 1000 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 1000 + 25 Reorder the terms: 25 + 10x + x2 = 1000 + 25 Combine like terms: 1000 + 25 = 1025 25 + 10x + x2 = 1025 Factor a perfect square on the left side: (x + 5)(x + 5) = 1025 Calculate the square root of the right side: 32.015621187 Break this problem into two subproblems by setting (x + 5) equal to 32.015621187 and -32.015621187.Subproblem 1
x + 5 = 32.015621187 Simplifying x + 5 = 32.015621187 Reorder the terms: 5 + x = 32.015621187 Solving 5 + x = 32.015621187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 32.015621187 + -5 Combine like terms: 5 + -5 = 0 0 + x = 32.015621187 + -5 x = 32.015621187 + -5 Combine like terms: 32.015621187 + -5 = 27.015621187 x = 27.015621187 Simplifying x = 27.015621187Subproblem 2
x + 5 = -32.015621187 Simplifying x + 5 = -32.015621187 Reorder the terms: 5 + x = -32.015621187 Solving 5 + x = -32.015621187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -32.015621187 + -5 Combine like terms: 5 + -5 = 0 0 + x = -32.015621187 + -5 x = -32.015621187 + -5 Combine like terms: -32.015621187 + -5 = -37.015621187 x = -37.015621187 Simplifying x = -37.015621187Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.015621187, -37.015621187}
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