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Simplifying x2 + -10x = 80x + 40 Reorder the terms: -10x + x2 = 80x + 40 Reorder the terms: -10x + x2 = 40 + 80x Solving -10x + x2 = 40 + 80x Solving for variable 'x'. Reorder the terms: -40 + -10x + -80x + x2 = 40 + 80x + -40 + -80x Combine like terms: -10x + -80x = -90x -40 + -90x + x2 = 40 + 80x + -40 + -80x Reorder the terms: -40 + -90x + x2 = 40 + -40 + 80x + -80x Combine like terms: 40 + -40 = 0 -40 + -90x + x2 = 0 + 80x + -80x -40 + -90x + x2 = 80x + -80x Combine like terms: 80x + -80x = 0 -40 + -90x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -90x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -90x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -90x + x2 = 0 + 40 -90x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -90x + x2 = 40 The x term is -90x. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90x + 2025 + x2 = 40 + 2025 Reorder the terms: 2025 + -90x + x2 = 40 + 2025 Combine like terms: 40 + 2025 = 2065 2025 + -90x + x2 = 2065 Factor a perfect square on the left side: (x + -45)(x + -45) = 2065 Calculate the square root of the right side: 45.44227107 Break this problem into two subproblems by setting (x + -45) equal to 45.44227107 and -45.44227107.Subproblem 1
x + -45 = 45.44227107 Simplifying x + -45 = 45.44227107 Reorder the terms: -45 + x = 45.44227107 Solving -45 + x = 45.44227107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = 45.44227107 + 45 Combine like terms: -45 + 45 = 0 0 + x = 45.44227107 + 45 x = 45.44227107 + 45 Combine like terms: 45.44227107 + 45 = 90.44227107 x = 90.44227107 Simplifying x = 90.44227107Subproblem 2
x + -45 = -45.44227107 Simplifying x + -45 = -45.44227107 Reorder the terms: -45 + x = -45.44227107 Solving -45 + x = -45.44227107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + x = -45.44227107 + 45 Combine like terms: -45 + 45 = 0 0 + x = -45.44227107 + 45 x = -45.44227107 + 45 Combine like terms: -45.44227107 + 45 = -0.44227107 x = -0.44227107 Simplifying x = -0.44227107Solution
The solution to the problem is based on the solutions from the subproblems. x = {90.44227107, -0.44227107}
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