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Simplifying (4x2 + 3x + -1) + -1(x2 + -6x + 8) = 0 Reorder the terms: (-1 + 3x + 4x2) + -1(x2 + -6x + 8) = 0 Remove parenthesis around (-1 + 3x + 4x2) -1 + 3x + 4x2 + -1(x2 + -6x + 8) = 0 Reorder the terms: -1 + 3x + 4x2 + -1(8 + -6x + x2) = 0 -1 + 3x + 4x2 + (8 * -1 + -6x * -1 + x2 * -1) = 0 -1 + 3x + 4x2 + (-8 + 6x + -1x2) = 0 Reorder the terms: -1 + -8 + 3x + 6x + 4x2 + -1x2 = 0 Combine like terms: -1 + -8 = -9 -9 + 3x + 6x + 4x2 + -1x2 = 0 Combine like terms: 3x + 6x = 9x -9 + 9x + 4x2 + -1x2 = 0 Combine like terms: 4x2 + -1x2 = 3x2 -9 + 9x + 3x2 = 0 Solving -9 + 9x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 3x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 3x + x2)' equal to zero and attempt to solve: Simplifying -3 + 3x + x2 = 0 Solving -3 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 3x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 3x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3x + x2 = 0 + 3 3x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 3x + x2 = 3 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 3 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + 3x + x2 = 5.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + 1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + 1.5 = 2.291287847 Simplifying x + 1.5 = 2.291287847 Reorder the terms: 1.5 + x = 2.291287847 Solving 1.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.291287847 + -1.5 x = 2.291287847 + -1.5 Combine like terms: 2.291287847 + -1.5 = 0.791287847 x = 0.791287847 Simplifying x = 0.791287847Subproblem 2
x + 1.5 = -2.291287847 Simplifying x + 1.5 = -2.291287847 Reorder the terms: 1.5 + x = -2.291287847 Solving 1.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.291287847 + -1.5 x = -2.291287847 + -1.5 Combine like terms: -2.291287847 + -1.5 = -3.791287847 x = -3.791287847 Simplifying x = -3.791287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.791287847, -3.791287847}Solution
x = {0.791287847, -3.791287847}
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