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Simplifying (4x2 + -6x + -7) + -2x2 + -6x + -3 = 0 Reorder the terms: (-7 + -6x + 4x2) + -2x2 + -6x + -3 = 0 Remove parenthesis around (-7 + -6x + 4x2) -7 + -6x + 4x2 + -2x2 + -6x + -3 = 0 Reorder the terms: -7 + -3 + -6x + -6x + 4x2 + -2x2 = 0 Combine like terms: -7 + -3 = -10 -10 + -6x + -6x + 4x2 + -2x2 = 0 Combine like terms: -6x + -6x = -12x -10 + -12x + 4x2 + -2x2 = 0 Combine like terms: 4x2 + -2x2 = 2x2 -10 + -12x + 2x2 = 0 Solving -10 + -12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -6x + x2)' equal to zero and attempt to solve: Simplifying -5 + -6x + x2 = 0 Solving -5 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -6x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -6x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6x + x2 = 0 + 5 -6x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -6x + x2 = 5 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 5 + 9 Reorder the terms: 9 + -6x + x2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + -6x + x2 = 14 Factor a perfect square on the left side: (x + -3)(x + -3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + -3) equal to 3.741657387 and -3.741657387.Subproblem 1
x + -3 = 3.741657387 Simplifying x + -3 = 3.741657387 Reorder the terms: -3 + x = 3.741657387 Solving -3 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.741657387 + 3 x = 3.741657387 + 3 Combine like terms: 3.741657387 + 3 = 6.741657387 x = 6.741657387 Simplifying x = 6.741657387Subproblem 2
x + -3 = -3.741657387 Simplifying x + -3 = -3.741657387 Reorder the terms: -3 + x = -3.741657387 Solving -3 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.741657387 + 3 x = -3.741657387 + 3 Combine like terms: -3.741657387 + 3 = -0.741657387 x = -0.741657387 Simplifying x = -0.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.741657387, -0.741657387}Solution
x = {6.741657387, -0.741657387}
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