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Simplifying (x2 + 5x + 4) + -1(6x2 + -7x + 5) = 0 Reorder the terms: (4 + 5x + x2) + -1(6x2 + -7x + 5) = 0 Remove parenthesis around (4 + 5x + x2) 4 + 5x + x2 + -1(6x2 + -7x + 5) = 0 Reorder the terms: 4 + 5x + x2 + -1(5 + -7x + 6x2) = 0 4 + 5x + x2 + (5 * -1 + -7x * -1 + 6x2 * -1) = 0 4 + 5x + x2 + (-5 + 7x + -6x2) = 0 Reorder the terms: 4 + -5 + 5x + 7x + x2 + -6x2 = 0 Combine like terms: 4 + -5 = -1 -1 + 5x + 7x + x2 + -6x2 = 0 Combine like terms: 5x + 7x = 12x -1 + 12x + x2 + -6x2 = 0 Combine like terms: x2 + -6x2 = -5x2 -1 + 12x + -5x2 = 0 Solving -1 + 12x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.2 + -2.4x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -2.4x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -2.4x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -2.4x + x2 = 0 + -0.2 -2.4x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -2.4x + x2 = -0.2 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -0.2 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -0.2 + 1.44 Combine like terms: -0.2 + 1.44 = 1.24 1.44 + -2.4x + x2 = 1.24 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (x + -1.2) equal to 1.113552873 and -1.113552873.Subproblem 1
x + -1.2 = 1.113552873 Simplifying x + -1.2 = 1.113552873 Reorder the terms: -1.2 + x = 1.113552873 Solving -1.2 + x = 1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 1.113552873 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.113552873 + 1.2 x = 1.113552873 + 1.2 Combine like terms: 1.113552873 + 1.2 = 2.313552873 x = 2.313552873 Simplifying x = 2.313552873Subproblem 2
x + -1.2 = -1.113552873 Simplifying x + -1.2 = -1.113552873 Reorder the terms: -1.2 + x = -1.113552873 Solving -1.2 + x = -1.113552873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -1.113552873 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.113552873 + 1.2 x = -1.113552873 + 1.2 Combine like terms: -1.113552873 + 1.2 = 0.086447127 x = 0.086447127 Simplifying x = 0.086447127Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.313552873, 0.086447127}
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