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Simplifying 0.9x2 + -90x + -1000 = 0 Reorder the terms: -1000 + -90x + 0.9x2 = 0 Solving -1000 + -90x + 0.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.9 the coefficient of the squared term: Divide each side by '0.9'. -1111.111111 + -100x + x2 = 0 Move the constant term to the right: Add '1111.111111' to each side of the equation. -1111.111111 + -100x + 1111.111111 + x2 = 0 + 1111.111111 Reorder the terms: -1111.111111 + 1111.111111 + -100x + x2 = 0 + 1111.111111 Combine like terms: -1111.111111 + 1111.111111 = 0.000000 0.000000 + -100x + x2 = 0 + 1111.111111 -100x + x2 = 0 + 1111.111111 Combine like terms: 0 + 1111.111111 = 1111.111111 -100x + x2 = 1111.111111 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = 1111.111111 + 2500 Reorder the terms: 2500 + -100x + x2 = 1111.111111 + 2500 Combine like terms: 1111.111111 + 2500 = 3611.111111 2500 + -100x + x2 = 3611.111111 Factor a perfect square on the left side: (x + -50)(x + -50) = 3611.111111 Calculate the square root of the right side: 60.092521257 Break this problem into two subproblems by setting (x + -50) equal to 60.092521257 and -60.092521257.Subproblem 1
x + -50 = 60.092521257 Simplifying x + -50 = 60.092521257 Reorder the terms: -50 + x = 60.092521257 Solving -50 + x = 60.092521257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 60.092521257 + 50 Combine like terms: -50 + 50 = 0 0 + x = 60.092521257 + 50 x = 60.092521257 + 50 Combine like terms: 60.092521257 + 50 = 110.092521257 x = 110.092521257 Simplifying x = 110.092521257Subproblem 2
x + -50 = -60.092521257 Simplifying x + -50 = -60.092521257 Reorder the terms: -50 + x = -60.092521257 Solving -50 + x = -60.092521257 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -60.092521257 + 50 Combine like terms: -50 + 50 = 0 0 + x = -60.092521257 + 50 x = -60.092521257 + 50 Combine like terms: -60.092521257 + 50 = -10.092521257 x = -10.092521257 Simplifying x = -10.092521257Solution
The solution to the problem is based on the solutions from the subproblems. x = {110.092521257, -10.092521257}
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