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Simplifying (4x2 + 5x + -6) + -1(2x2 + -1x + -4) = 0 Reorder the terms: (-6 + 5x + 4x2) + -1(2x2 + -1x + -4) = 0 Remove parenthesis around (-6 + 5x + 4x2) -6 + 5x + 4x2 + -1(2x2 + -1x + -4) = 0 Reorder the terms: -6 + 5x + 4x2 + -1(-4 + -1x + 2x2) = 0 -6 + 5x + 4x2 + (-4 * -1 + -1x * -1 + 2x2 * -1) = 0 -6 + 5x + 4x2 + (4 + 1x + -2x2) = 0 Reorder the terms: -6 + 4 + 5x + 1x + 4x2 + -2x2 = 0 Combine like terms: -6 + 4 = -2 -2 + 5x + 1x + 4x2 + -2x2 = 0 Combine like terms: 5x + 1x = 6x -2 + 6x + 4x2 + -2x2 = 0 Combine like terms: 4x2 + -2x2 = 2x2 -2 + 6x + 2x2 = 0 Solving -2 + 6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 3x + x2)' equal to zero and attempt to solve: Simplifying -1 + 3x + x2 = 0 Solving -1 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 3x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 3x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3x + x2 = 0 + 1 3x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 3x + x2 = 1 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 = 1 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 1 + 2.25 Combine like terms: 1 + 2.25 = 3.25 2.25 + 3x + x2 = 3.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + 1.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + 1.5 = 1.802775638 Simplifying x + 1.5 = 1.802775638 Reorder the terms: 1.5 + x = 1.802775638 Solving 1.5 + x = 1.802775638 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 = 1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.802775638 + -1.5 x = 1.802775638 + -1.5 Combine like terms: 1.802775638 + -1.5 = 0.302775638 x = 0.302775638 Simplifying x = 0.302775638Subproblem 2
x + 1.5 = -1.802775638 Simplifying x + 1.5 = -1.802775638 Reorder the terms: 1.5 + x = -1.802775638 Solving 1.5 + x = -1.802775638 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 = -1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.802775638 + -1.5 x = -1.802775638 + -1.5 Combine like terms: -1.802775638 + -1.5 = -3.302775638 x = -3.302775638 Simplifying x = -3.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.302775638, -3.302775638}Solution
x = {0.302775638, -3.302775638}
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