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Simplifying 3x2 + 3x = x2 + -5x + 4 Reorder the terms: 3x + 3x2 = x2 + -5x + 4 Reorder the terms: 3x + 3x2 = 4 + -5x + x2 Solving 3x + 3x2 = 4 + -5x + x2 Solving for variable 'x'. Reorder the terms: -4 + 3x + 5x + 3x2 + -1x2 = 4 + -5x + x2 + -4 + 5x + -1x2 Combine like terms: 3x + 5x = 8x -4 + 8x + 3x2 + -1x2 = 4 + -5x + x2 + -4 + 5x + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -4 + 8x + 2x2 = 4 + -5x + x2 + -4 + 5x + -1x2 Reorder the terms: -4 + 8x + 2x2 = 4 + -4 + -5x + 5x + x2 + -1x2 Combine like terms: 4 + -4 = 0 -4 + 8x + 2x2 = 0 + -5x + 5x + x2 + -1x2 -4 + 8x + 2x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 -4 + 8x + 2x2 = 0 + x2 + -1x2 -4 + 8x + 2x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 4x + x2)' equal to zero and attempt to solve: Simplifying -2 + 4x + x2 = 0 Solving -2 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 4x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 4x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4x + x2 = 0 + 2 4x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 4x + x2 = 2 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 = 2 + 4 Reorder the terms: 4 + 4x + x2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + 4x + x2 = 6 Factor a perfect square on the left side: (x + 2)(x + 2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 2) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 2 = 2.449489743 Simplifying x + 2 = 2.449489743 Reorder the terms: 2 + x = 2.449489743 Solving 2 + x = 2.449489743 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 = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.449489743 + -2 x = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 x = 0.449489743 Simplifying x = 0.449489743Subproblem 2
x + 2 = -2.449489743 Simplifying x + 2 = -2.449489743 Reorder the terms: 2 + x = -2.449489743 Solving 2 + x = -2.449489743 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 = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.449489743 + -2 x = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 x = -4.449489743 Simplifying x = -4.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.449489743, -4.449489743}Solution
x = {0.449489743, -4.449489743}
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