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Simplifying 530x + -15000 + -1x2 = 20 Reorder the terms: -15000 + 530x + -1x2 = 20 Solving -15000 + 530x + -1x2 = 20 Solving for variable 'x'. Reorder the terms: -15000 + -20 + 530x + -1x2 = 20 + -20 Combine like terms: -15000 + -20 = -15020 -15020 + 530x + -1x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -15020 + 530x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 15020 + -530x + x2 = 0 Move the constant term to the right: Add '-15020' to each side of the equation. 15020 + -530x + -15020 + x2 = 0 + -15020 Reorder the terms: 15020 + -15020 + -530x + x2 = 0 + -15020 Combine like terms: 15020 + -15020 = 0 0 + -530x + x2 = 0 + -15020 -530x + x2 = 0 + -15020 Combine like terms: 0 + -15020 = -15020 -530x + x2 = -15020 The x term is -530x. Take half its coefficient (-265). Square it (70225) and add it to both sides. Add '70225' to each side of the equation. -530x + 70225 + x2 = -15020 + 70225 Reorder the terms: 70225 + -530x + x2 = -15020 + 70225 Combine like terms: -15020 + 70225 = 55205 70225 + -530x + x2 = 55205 Factor a perfect square on the left side: (x + -265)(x + -265) = 55205 Calculate the square root of the right side: 234.957442955 Break this problem into two subproblems by setting (x + -265) equal to 234.957442955 and -234.957442955.Subproblem 1
x + -265 = 234.957442955 Simplifying x + -265 = 234.957442955 Reorder the terms: -265 + x = 234.957442955 Solving -265 + x = 234.957442955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '265' to each side of the equation. -265 + 265 + x = 234.957442955 + 265 Combine like terms: -265 + 265 = 0 0 + x = 234.957442955 + 265 x = 234.957442955 + 265 Combine like terms: 234.957442955 + 265 = 499.957442955 x = 499.957442955 Simplifying x = 499.957442955Subproblem 2
x + -265 = -234.957442955 Simplifying x + -265 = -234.957442955 Reorder the terms: -265 + x = -234.957442955 Solving -265 + x = -234.957442955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '265' to each side of the equation. -265 + 265 + x = -234.957442955 + 265 Combine like terms: -265 + 265 = 0 0 + x = -234.957442955 + 265 x = -234.957442955 + 265 Combine like terms: -234.957442955 + 265 = 30.042557045 x = 30.042557045 Simplifying x = 30.042557045Solution
The solution to the problem is based on the solutions from the subproblems. x = {499.957442955, 30.042557045}
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