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Simplifying 170x + -1x2 + -1000 = 0 Reorder the terms: -1000 + 170x + -1x2 = 0 Solving -1000 + 170x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1000 + -170x + x2 = 0 Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + -170x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -170x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -170x + x2 = 0 + -1000 -170x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -170x + x2 = -1000 The x term is -170x. Take half its coefficient (-85). Square it (7225) and add it to both sides. Add '7225' to each side of the equation. -170x + 7225 + x2 = -1000 + 7225 Reorder the terms: 7225 + -170x + x2 = -1000 + 7225 Combine like terms: -1000 + 7225 = 6225 7225 + -170x + x2 = 6225 Factor a perfect square on the left side: (x + -85)(x + -85) = 6225 Calculate the square root of the right side: 78.89866919 Break this problem into two subproblems by setting (x + -85) equal to 78.89866919 and -78.89866919.Subproblem 1
x + -85 = 78.89866919 Simplifying x + -85 = 78.89866919 Reorder the terms: -85 + x = 78.89866919 Solving -85 + x = 78.89866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '85' to each side of the equation. -85 + 85 + x = 78.89866919 + 85 Combine like terms: -85 + 85 = 0 0 + x = 78.89866919 + 85 x = 78.89866919 + 85 Combine like terms: 78.89866919 + 85 = 163.89866919 x = 163.89866919 Simplifying x = 163.89866919Subproblem 2
x + -85 = -78.89866919 Simplifying x + -85 = -78.89866919 Reorder the terms: -85 + x = -78.89866919 Solving -85 + x = -78.89866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '85' to each side of the equation. -85 + 85 + x = -78.89866919 + 85 Combine like terms: -85 + 85 = 0 0 + x = -78.89866919 + 85 x = -78.89866919 + 85 Combine like terms: -78.89866919 + 85 = 6.10133081 x = 6.10133081 Simplifying x = 6.10133081Solution
The solution to the problem is based on the solutions from the subproblems. x = {163.89866919, 6.10133081}
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