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Simplifying 3x2 + -3x + -4x2 + 2x + 5 = 0 Reorder the terms: 5 + -3x + 2x + 3x2 + -4x2 = 0 Combine like terms: -3x + 2x = -1x 5 + -1x + 3x2 + -4x2 = 0 Combine like terms: 3x2 + -4x2 = -1x2 5 + -1x + -1x2 = 0 Solving 5 + -1x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x + x2 = 0 + 5 x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 x + x2 = 5 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. + 0.25 + x2 = 5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 1.25 + x2 = 5.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + 0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + 0.5 = 2.291287847 Simplifying x + 0.5 = 2.291287847 Reorder the terms: 0.5 + x = 2.291287847 Solving 0.5 + x = 2.291287847 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 = 2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.291287847 + -0.5 x = 2.291287847 + -0.5 Combine like terms: 2.291287847 + -0.5 = 1.791287847 x = 1.791287847 Simplifying x = 1.791287847Subproblem 2
x + 0.5 = -2.291287847 Simplifying x + 0.5 = -2.291287847 Reorder the terms: 0.5 + x = -2.291287847 Solving 0.5 + x = -2.291287847 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 = -2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.291287847 + -0.5 x = -2.291287847 + -0.5 Combine like terms: -2.291287847 + -0.5 = -2.791287847 x = -2.791287847 Simplifying x = -2.791287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.791287847, -2.791287847}
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