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Simplifying 3x2 + 4x + -10 = 2x2 + 14 Reorder the terms: -10 + 4x + 3x2 = 2x2 + 14 Reorder the terms: -10 + 4x + 3x2 = 14 + 2x2 Solving -10 + 4x + 3x2 = 14 + 2x2 Solving for variable 'x'. Reorder the terms: -10 + -14 + 4x + 3x2 + -2x2 = 14 + 2x2 + -14 + -2x2 Combine like terms: -10 + -14 = -24 -24 + 4x + 3x2 + -2x2 = 14 + 2x2 + -14 + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -24 + 4x + 1x2 = 14 + 2x2 + -14 + -2x2 Reorder the terms: -24 + 4x + 1x2 = 14 + -14 + 2x2 + -2x2 Combine like terms: 14 + -14 = 0 -24 + 4x + 1x2 = 0 + 2x2 + -2x2 -24 + 4x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -24 + 4x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 4x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 4x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 4x + x2 = 0 + 24 4x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 4x + x2 = 24 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 24 + 4 Reorder the terms: 4 + 4x + x2 = 24 + 4 Combine like terms: 24 + 4 = 28 4 + 4x + x2 = 28 Factor a perfect square on the left side: (x + 2)(x + 2) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + 2) equal to 5.291502622 and -5.291502622.Subproblem 1
x + 2 = 5.291502622 Simplifying x + 2 = 5.291502622 Reorder the terms: 2 + x = 5.291502622 Solving 2 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 5.291502622 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.291502622 + -2 x = 5.291502622 + -2 Combine like terms: 5.291502622 + -2 = 3.291502622 x = 3.291502622 Simplifying x = 3.291502622Subproblem 2
x + 2 = -5.291502622 Simplifying x + 2 = -5.291502622 Reorder the terms: 2 + x = -5.291502622 Solving 2 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -5.291502622 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.291502622 + -2 x = -5.291502622 + -2 Combine like terms: -5.291502622 + -2 = -7.291502622 x = -7.291502622 Simplifying x = -7.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.291502622, -7.291502622}
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