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Simplifying 3x2 + 90x + -1000 = 0 Reorder the terms: -1000 + 90x + 3x2 = 0 Solving -1000 + 90x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -333.3333333 + 30x + x2 = 0 Move the constant term to the right: Add '333.3333333' to each side of the equation. -333.3333333 + 30x + 333.3333333 + x2 = 0 + 333.3333333 Reorder the terms: -333.3333333 + 333.3333333 + 30x + x2 = 0 + 333.3333333 Combine like terms: -333.3333333 + 333.3333333 = 0.0000000 0.0000000 + 30x + x2 = 0 + 333.3333333 30x + x2 = 0 + 333.3333333 Combine like terms: 0 + 333.3333333 = 333.3333333 30x + x2 = 333.3333333 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 333.3333333 + 225 Reorder the terms: 225 + 30x + x2 = 333.3333333 + 225 Combine like terms: 333.3333333 + 225 = 558.3333333 225 + 30x + x2 = 558.3333333 Factor a perfect square on the left side: (x + 15)(x + 15) = 558.3333333 Calculate the square root of the right side: 23.629078131 Break this problem into two subproblems by setting (x + 15) equal to 23.629078131 and -23.629078131.Subproblem 1
x + 15 = 23.629078131 Simplifying x + 15 = 23.629078131 Reorder the terms: 15 + x = 23.629078131 Solving 15 + x = 23.629078131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 23.629078131 + -15 Combine like terms: 15 + -15 = 0 0 + x = 23.629078131 + -15 x = 23.629078131 + -15 Combine like terms: 23.629078131 + -15 = 8.629078131 x = 8.629078131 Simplifying x = 8.629078131Subproblem 2
x + 15 = -23.629078131 Simplifying x + 15 = -23.629078131 Reorder the terms: 15 + x = -23.629078131 Solving 15 + x = -23.629078131 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -23.629078131 + -15 Combine like terms: 15 + -15 = 0 0 + x = -23.629078131 + -15 x = -23.629078131 + -15 Combine like terms: -23.629078131 + -15 = -38.629078131 x = -38.629078131 Simplifying x = -38.629078131Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.629078131, -38.629078131}
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