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Simplifying x2 + -290x + -90200 = 0 Reorder the terms: -90200 + -290x + x2 = 0 Solving -90200 + -290x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '90200' to each side of the equation. -90200 + -290x + 90200 + x2 = 0 + 90200 Reorder the terms: -90200 + 90200 + -290x + x2 = 0 + 90200 Combine like terms: -90200 + 90200 = 0 0 + -290x + x2 = 0 + 90200 -290x + x2 = 0 + 90200 Combine like terms: 0 + 90200 = 90200 -290x + x2 = 90200 The x term is -290x. Take half its coefficient (-145). Square it (21025) and add it to both sides. Add '21025' to each side of the equation. -290x + 21025 + x2 = 90200 + 21025 Reorder the terms: 21025 + -290x + x2 = 90200 + 21025 Combine like terms: 90200 + 21025 = 111225 21025 + -290x + x2 = 111225 Factor a perfect square on the left side: (x + -145)(x + -145) = 111225 Calculate the square root of the right side: 333.504122913 Break this problem into two subproblems by setting (x + -145) equal to 333.504122913 and -333.504122913.Subproblem 1
x + -145 = 333.504122913 Simplifying x + -145 = 333.504122913 Reorder the terms: -145 + x = 333.504122913 Solving -145 + x = 333.504122913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '145' to each side of the equation. -145 + 145 + x = 333.504122913 + 145 Combine like terms: -145 + 145 = 0 0 + x = 333.504122913 + 145 x = 333.504122913 + 145 Combine like terms: 333.504122913 + 145 = 478.504122913 x = 478.504122913 Simplifying x = 478.504122913Subproblem 2
x + -145 = -333.504122913 Simplifying x + -145 = -333.504122913 Reorder the terms: -145 + x = -333.504122913 Solving -145 + x = -333.504122913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '145' to each side of the equation. -145 + 145 + x = -333.504122913 + 145 Combine like terms: -145 + 145 = 0 0 + x = -333.504122913 + 145 x = -333.504122913 + 145 Combine like terms: -333.504122913 + 145 = -188.504122913 x = -188.504122913 Simplifying x = -188.504122913Solution
The solution to the problem is based on the solutions from the subproblems. x = {478.504122913, -188.504122913}
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