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Simplifying 1000 + 3x = x2 Solving 1000 + 3x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 1000 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1000 + -3x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -3x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -3x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -3x + x2 = 0 + 1000 -3x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -3x + x2 = 1000 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 = 1000 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1000 + 2.25 Combine like terms: 1000 + 2.25 = 1002.25 2.25 + -3x + x2 = 1002.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1002.25 Calculate the square root of the right side: 31.658332237 Break this problem into two subproblems by setting (x + -1.5) equal to 31.658332237 and -31.658332237.Subproblem 1
x + -1.5 = 31.658332237 Simplifying x + -1.5 = 31.658332237 Reorder the terms: -1.5 + x = 31.658332237 Solving -1.5 + x = 31.658332237 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 = 31.658332237 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 31.658332237 + 1.5 x = 31.658332237 + 1.5 Combine like terms: 31.658332237 + 1.5 = 33.158332237 x = 33.158332237 Simplifying x = 33.158332237Subproblem 2
x + -1.5 = -31.658332237 Simplifying x + -1.5 = -31.658332237 Reorder the terms: -1.5 + x = -31.658332237 Solving -1.5 + x = -31.658332237 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 = -31.658332237 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -31.658332237 + 1.5 x = -31.658332237 + 1.5 Combine like terms: -31.658332237 + 1.5 = -30.158332237 x = -30.158332237 Simplifying x = -30.158332237Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.158332237, -30.158332237}
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