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Simplifying 3x2 + -12 = -2x2 + 5x + 12 Reorder the terms: -12 + 3x2 = -2x2 + 5x + 12 Reorder the terms: -12 + 3x2 = 12 + 5x + -2x2 Solving -12 + 3x2 = 12 + 5x + -2x2 Solving for variable 'x'. Reorder the terms: -12 + -12 + -5x + 3x2 + 2x2 = 12 + 5x + -2x2 + -12 + -5x + 2x2 Combine like terms: -12 + -12 = -24 -24 + -5x + 3x2 + 2x2 = 12 + 5x + -2x2 + -12 + -5x + 2x2 Combine like terms: 3x2 + 2x2 = 5x2 -24 + -5x + 5x2 = 12 + 5x + -2x2 + -12 + -5x + 2x2 Reorder the terms: -24 + -5x + 5x2 = 12 + -12 + 5x + -5x + -2x2 + 2x2 Combine like terms: 12 + -12 = 0 -24 + -5x + 5x2 = 0 + 5x + -5x + -2x2 + 2x2 -24 + -5x + 5x2 = 5x + -5x + -2x2 + 2x2 Combine like terms: 5x + -5x = 0 -24 + -5x + 5x2 = 0 + -2x2 + 2x2 -24 + -5x + 5x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -24 + -5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.8 + -1x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -1x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -1x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -1x + x2 = 0 + 4.8 -1x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -1x + x2 = 4.8 The x term is -1x. 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. -1x + 0.25 + x2 = 4.8 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 4.8 + 0.25 Combine like terms: 4.8 + 0.25 = 5.05 0.25 + -1x + x2 = 5.05 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 5.05 Calculate the square root of the right side: 2.247220505 Break this problem into two subproblems by setting (x + -0.5) equal to 2.247220505 and -2.247220505.Subproblem 1
x + -0.5 = 2.247220505 Simplifying x + -0.5 = 2.247220505 Reorder the terms: -0.5 + x = 2.247220505 Solving -0.5 + x = 2.247220505 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 = 2.247220505 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.247220505 + 0.5 x = 2.247220505 + 0.5 Combine like terms: 2.247220505 + 0.5 = 2.747220505 x = 2.747220505 Simplifying x = 2.747220505Subproblem 2
x + -0.5 = -2.247220505 Simplifying x + -0.5 = -2.247220505 Reorder the terms: -0.5 + x = -2.247220505 Solving -0.5 + x = -2.247220505 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 = -2.247220505 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.247220505 + 0.5 x = -2.247220505 + 0.5 Combine like terms: -2.247220505 + 0.5 = -1.747220505 x = -1.747220505 Simplifying x = -1.747220505Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.747220505, -1.747220505}
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