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Simplifying x = x2 + 10x + -75 Reorder the terms: x = -75 + 10x + x2 Solving x = -75 + 10x + x2 Solving for variable 'x'. Reorder the terms: 75 + x + -10x + -1x2 = -75 + 10x + x2 + 75 + -10x + -1x2 Combine like terms: x + -10x = -9x 75 + -9x + -1x2 = -75 + 10x + x2 + 75 + -10x + -1x2 Reorder the terms: 75 + -9x + -1x2 = -75 + 75 + 10x + -10x + x2 + -1x2 Combine like terms: -75 + 75 = 0 75 + -9x + -1x2 = 0 + 10x + -10x + x2 + -1x2 75 + -9x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 75 + -9x + -1x2 = 0 + x2 + -1x2 75 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 75 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -75 + 9x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 9x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 9x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 9x + x2 = 0 + 75 9x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 9x + x2 = 75 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 75 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 75 + 20.25 Combine like terms: 75 + 20.25 = 95.25 20.25 + 9x + x2 = 95.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 95.25 Calculate the square root of the right side: 9.759610648 Break this problem into two subproblems by setting (x + 4.5) equal to 9.759610648 and -9.759610648.Subproblem 1
x + 4.5 = 9.759610648 Simplifying x + 4.5 = 9.759610648 Reorder the terms: 4.5 + x = 9.759610648 Solving 4.5 + x = 9.759610648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 9.759610648 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 9.759610648 + -4.5 x = 9.759610648 + -4.5 Combine like terms: 9.759610648 + -4.5 = 5.259610648 x = 5.259610648 Simplifying x = 5.259610648Subproblem 2
x + 4.5 = -9.759610648 Simplifying x + 4.5 = -9.759610648 Reorder the terms: 4.5 + x = -9.759610648 Solving 4.5 + x = -9.759610648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -9.759610648 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -9.759610648 + -4.5 x = -9.759610648 + -4.5 Combine like terms: -9.759610648 + -4.5 = -14.259610648 x = -14.259610648 Simplifying x = -14.259610648Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.259610648, -14.259610648}
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