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Simplifying 9x2 + 9 = 24 + 3x + -1x2 Reorder the terms: 9 + 9x2 = 24 + 3x + -1x2 Solving 9 + 9x2 = 24 + 3x + -1x2 Solving for variable 'x'. Reorder the terms: 9 + -24 + -3x + 9x2 + x2 = 24 + 3x + -1x2 + -24 + -3x + x2 Combine like terms: 9 + -24 = -15 -15 + -3x + 9x2 + x2 = 24 + 3x + -1x2 + -24 + -3x + x2 Combine like terms: 9x2 + x2 = 10x2 -15 + -3x + 10x2 = 24 + 3x + -1x2 + -24 + -3x + x2 Reorder the terms: -15 + -3x + 10x2 = 24 + -24 + 3x + -3x + -1x2 + x2 Combine like terms: 24 + -24 = 0 -15 + -3x + 10x2 = 0 + 3x + -3x + -1x2 + x2 -15 + -3x + 10x2 = 3x + -3x + -1x2 + x2 Combine like terms: 3x + -3x = 0 -15 + -3x + 10x2 = 0 + -1x2 + x2 -15 + -3x + 10x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -15 + -3x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.5 + -0.3x + x2 = 0.0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.3x + 1.5 + x2 = 0.0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.3x + x2 = 0.0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.3x + x2 = 0.0 + 1.5 -0.3x + x2 = 0.0 + 1.5 Combine like terms: 0.0 + 1.5 = 1.5 -0.3x + x2 = 1.5 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 1.5 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 1.5 + 0.0225 Combine like terms: 1.5 + 0.0225 = 1.5225 0.0225 + -0.3x + x2 = 1.5225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 1.5225 Calculate the square root of the right side: 1.233896268 Break this problem into two subproblems by setting (x + -0.15) equal to 1.233896268 and -1.233896268.Subproblem 1
x + -0.15 = 1.233896268 Simplifying x + -0.15 = 1.233896268 Reorder the terms: -0.15 + x = 1.233896268 Solving -0.15 + x = 1.233896268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 1.233896268 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 1.233896268 + 0.15 x = 1.233896268 + 0.15 Combine like terms: 1.233896268 + 0.15 = 1.383896268 x = 1.383896268 Simplifying x = 1.383896268Subproblem 2
x + -0.15 = -1.233896268 Simplifying x + -0.15 = -1.233896268 Reorder the terms: -0.15 + x = -1.233896268 Solving -0.15 + x = -1.233896268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -1.233896268 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -1.233896268 + 0.15 x = -1.233896268 + 0.15 Combine like terms: -1.233896268 + 0.15 = -1.083896268 x = -1.083896268 Simplifying x = -1.083896268Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.383896268, -1.083896268}
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