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Simplifying x(3x + 6x + -9 + x) = 93 Reorder the terms: x(-9 + 3x + 6x + x) = 93 Combine like terms: 3x + 6x = 9x x(-9 + 9x + x) = 93 Combine like terms: 9x + x = 10x x(-9 + 10x) = 93 (-9 * x + 10x * x) = 93 (-9x + 10x2) = 93 Solving -9x + 10x2 = 93 Solving for variable 'x'. Reorder the terms: -93 + -9x + 10x2 = 93 + -93 Combine like terms: 93 + -93 = 0 -93 + -9x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -9.3 + -0.9x + x2 = 0.0 Move the constant term to the right: Add '9.3' to each side of the equation. -9.3 + -0.9x + 9.3 + x2 = 0.0 + 9.3 Reorder the terms: -9.3 + 9.3 + -0.9x + x2 = 0.0 + 9.3 Combine like terms: -9.3 + 9.3 = 0.0 0.0 + -0.9x + x2 = 0.0 + 9.3 -0.9x + x2 = 0.0 + 9.3 Combine like terms: 0.0 + 9.3 = 9.3 -0.9x + x2 = 9.3 The x term is -0.9x. Take half its coefficient (-0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. -0.9x + 0.2025 + x2 = 9.3 + 0.2025 Reorder the terms: 0.2025 + -0.9x + x2 = 9.3 + 0.2025 Combine like terms: 9.3 + 0.2025 = 9.5025 0.2025 + -0.9x + x2 = 9.5025 Factor a perfect square on the left side: (x + -0.45)(x + -0.45) = 9.5025 Calculate the square root of the right side: 3.082612528 Break this problem into two subproblems by setting (x + -0.45) equal to 3.082612528 and -3.082612528.Subproblem 1
x + -0.45 = 3.082612528 Simplifying x + -0.45 = 3.082612528 Reorder the terms: -0.45 + x = 3.082612528 Solving -0.45 + x = 3.082612528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = 3.082612528 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 3.082612528 + 0.45 x = 3.082612528 + 0.45 Combine like terms: 3.082612528 + 0.45 = 3.532612528 x = 3.532612528 Simplifying x = 3.532612528Subproblem 2
x + -0.45 = -3.082612528 Simplifying x + -0.45 = -3.082612528 Reorder the terms: -0.45 + x = -3.082612528 Solving -0.45 + x = -3.082612528 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.45' to each side of the equation. -0.45 + 0.45 + x = -3.082612528 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -3.082612528 + 0.45 x = -3.082612528 + 0.45 Combine like terms: -3.082612528 + 0.45 = -2.632612528 x = -2.632612528 Simplifying x = -2.632612528Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.532612528, -2.632612528}
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