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Simplifying (-4x2 + -3x + 2) + (6x2 + -7x) = 0 Reorder the terms: (2 + -3x + -4x2) + (6x2 + -7x) = 0 Remove parenthesis around (2 + -3x + -4x2) 2 + -3x + -4x2 + (6x2 + -7x) = 0 Reorder the terms: 2 + -3x + -4x2 + (-7x + 6x2) = 0 Remove parenthesis around (-7x + 6x2) 2 + -3x + -4x2 + -7x + 6x2 = 0 Reorder the terms: 2 + -3x + -7x + -4x2 + 6x2 = 0 Combine like terms: -3x + -7x = -10x 2 + -10x + -4x2 + 6x2 = 0 Combine like terms: -4x2 + 6x2 = 2x2 2 + -10x + 2x2 = 0 Solving 2 + -10x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -5x + x2)' equal to zero and attempt to solve: Simplifying 1 + -5x + x2 = 0 Solving 1 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x + x2 = 0 + -1 -5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5x + x2 = -1 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -1 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -1 + 6.25 Combine like terms: -1 + 6.25 = 5.25 6.25 + -5x + x2 = 5.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -2.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + -2.5 = 2.291287847 Simplifying x + -2.5 = 2.291287847 Reorder the terms: -2.5 + x = 2.291287847 Solving -2.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.291287847 + 2.5 x = 2.291287847 + 2.5 Combine like terms: 2.291287847 + 2.5 = 4.791287847 x = 4.791287847 Simplifying x = 4.791287847Subproblem 2
x + -2.5 = -2.291287847 Simplifying x + -2.5 = -2.291287847 Reorder the terms: -2.5 + x = -2.291287847 Solving -2.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.291287847 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.291287847 + 2.5 x = -2.291287847 + 2.5 Combine like terms: -2.291287847 + 2.5 = 0.208712153 x = 0.208712153 Simplifying x = 0.208712153Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.791287847, 0.208712153}Solution
x = {4.791287847, 0.208712153}
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