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Simplifying 4x + 4 = 76 + 4x + 19x + x2 Reorder the terms: 4 + 4x = 76 + 4x + 19x + x2 Combine like terms: 4x + 19x = 23x 4 + 4x = 76 + 23x + x2 Solving 4 + 4x = 76 + 23x + x2 Solving for variable 'x'. Reorder the terms: 4 + -76 + 4x + -23x + -1x2 = 76 + 23x + x2 + -76 + -23x + -1x2 Combine like terms: 4 + -76 = -72 -72 + 4x + -23x + -1x2 = 76 + 23x + x2 + -76 + -23x + -1x2 Combine like terms: 4x + -23x = -19x -72 + -19x + -1x2 = 76 + 23x + x2 + -76 + -23x + -1x2 Reorder the terms: -72 + -19x + -1x2 = 76 + -76 + 23x + -23x + x2 + -1x2 Combine like terms: 76 + -76 = 0 -72 + -19x + -1x2 = 0 + 23x + -23x + x2 + -1x2 -72 + -19x + -1x2 = 23x + -23x + x2 + -1x2 Combine like terms: 23x + -23x = 0 -72 + -19x + -1x2 = 0 + x2 + -1x2 -72 + -19x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -72 + -19x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(72 + 19x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(72 + 19x + x2)' equal to zero and attempt to solve: Simplifying 72 + 19x + x2 = 0 Solving 72 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + 19x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + 19x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + 19x + x2 = 0 + -72 19x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 19x + x2 = -72 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -72 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -72 + 90.25 Combine like terms: -72 + 90.25 = 18.25 90.25 + 19x + x2 = 18.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + 9.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + 9.5 = 4.272001873 Simplifying x + 9.5 = 4.272001873 Reorder the terms: 9.5 + x = 4.272001873 Solving 9.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 4.272001873 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 4.272001873 + -9.5 x = 4.272001873 + -9.5 Combine like terms: 4.272001873 + -9.5 = -5.227998127 x = -5.227998127 Simplifying x = -5.227998127Subproblem 2
x + 9.5 = -4.272001873 Simplifying x + 9.5 = -4.272001873 Reorder the terms: 9.5 + x = -4.272001873 Solving 9.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -4.272001873 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -4.272001873 + -9.5 x = -4.272001873 + -9.5 Combine like terms: -4.272001873 + -9.5 = -13.772001873 x = -13.772001873 Simplifying x = -13.772001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.227998127, -13.772001873}Solution
x = {-5.227998127, -13.772001873}
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