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Simplifying x2 + -343x + 2867 = 0 Reorder the terms: 2867 + -343x + x2 = 0 Solving 2867 + -343x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2867' to each side of the equation. 2867 + -343x + -2867 + x2 = 0 + -2867 Reorder the terms: 2867 + -2867 + -343x + x2 = 0 + -2867 Combine like terms: 2867 + -2867 = 0 0 + -343x + x2 = 0 + -2867 -343x + x2 = 0 + -2867 Combine like terms: 0 + -2867 = -2867 -343x + x2 = -2867 The x term is -343x. Take half its coefficient (-171.5). Square it (29412.25) and add it to both sides. Add '29412.25' to each side of the equation. -343x + 29412.25 + x2 = -2867 + 29412.25 Reorder the terms: 29412.25 + -343x + x2 = -2867 + 29412.25 Combine like terms: -2867 + 29412.25 = 26545.25 29412.25 + -343x + x2 = 26545.25 Factor a perfect square on the left side: (x + -171.5)(x + -171.5) = 26545.25 Calculate the square root of the right side: 162.927130951 Break this problem into two subproblems by setting (x + -171.5) equal to 162.927130951 and -162.927130951.Subproblem 1
x + -171.5 = 162.927130951 Simplifying x + -171.5 = 162.927130951 Reorder the terms: -171.5 + x = 162.927130951 Solving -171.5 + x = 162.927130951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '171.5' to each side of the equation. -171.5 + 171.5 + x = 162.927130951 + 171.5 Combine like terms: -171.5 + 171.5 = 0.0 0.0 + x = 162.927130951 + 171.5 x = 162.927130951 + 171.5 Combine like terms: 162.927130951 + 171.5 = 334.427130951 x = 334.427130951 Simplifying x = 334.427130951Subproblem 2
x + -171.5 = -162.927130951 Simplifying x + -171.5 = -162.927130951 Reorder the terms: -171.5 + x = -162.927130951 Solving -171.5 + x = -162.927130951 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '171.5' to each side of the equation. -171.5 + 171.5 + x = -162.927130951 + 171.5 Combine like terms: -171.5 + 171.5 = 0.0 0.0 + x = -162.927130951 + 171.5 x = -162.927130951 + 171.5 Combine like terms: -162.927130951 + 171.5 = 8.572869049 x = 8.572869049 Simplifying x = 8.572869049Solution
The solution to the problem is based on the solutions from the subproblems. x = {334.427130951, 8.572869049}
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