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Simplifying 2x2 + x + -3 = 45 Reorder the terms: -3 + x + 2x2 = 45 Solving -3 + x + 2x2 = 45 Solving for variable 'x'. Reorder the terms: -3 + -45 + x + 2x2 = 45 + -45 Combine like terms: -3 + -45 = -48 -48 + x + 2x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -48 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -24 + 0.5x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 0.5x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 0.5x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 0.5x + x2 = 0 + 24 0.5x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 0.5x + x2 = 24 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 24 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 24 + 0.25 Combine like terms: 24 + 0.25 = 24.25 0.25 + 0.5x + x2 = 24.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x + 0.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x + 0.5 = 4.924428901 Simplifying x + 0.5 = 4.924428901 Reorder the terms: 0.5 + x = 4.924428901 Solving 0.5 + x = 4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.924428901 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.924428901 + -0.5 x = 4.924428901 + -0.5 Combine like terms: 4.924428901 + -0.5 = 4.424428901 x = 4.424428901 Simplifying x = 4.424428901Subproblem 2
x + 0.5 = -4.924428901 Simplifying x + 0.5 = -4.924428901 Reorder the terms: 0.5 + x = -4.924428901 Solving 0.5 + x = -4.924428901 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.924428901 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.924428901 + -0.5 x = -4.924428901 + -0.5 Combine like terms: -4.924428901 + -0.5 = -5.424428901 x = -5.424428901 Simplifying x = -5.424428901Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.424428901, -5.424428901}
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