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Simplifying 5x + 15 + (x + -2)(x + 4) = 12x + 19 Reorder the terms: 5x + 15 + (-2 + x)(x + 4) = 12x + 19 Reorder the terms: 5x + 15 + (-2 + x)(4 + x) = 12x + 19 Multiply (-2 + x) * (4 + x) 5x + 15 + (-2(4 + x) + x(4 + x)) = 12x + 19 5x + 15 + ((4 * -2 + x * -2) + x(4 + x)) = 12x + 19 5x + 15 + ((-8 + -2x) + x(4 + x)) = 12x + 19 5x + 15 + (-8 + -2x + (4 * x + x * x)) = 12x + 19 5x + 15 + (-8 + -2x + (4x + x2)) = 12x + 19 Combine like terms: -2x + 4x = 2x 5x + 15 + (-8 + 2x + x2) = 12x + 19 Reorder the terms: 15 + -8 + 5x + 2x + x2 = 12x + 19 Combine like terms: 15 + -8 = 7 7 + 5x + 2x + x2 = 12x + 19 Combine like terms: 5x + 2x = 7x 7 + 7x + x2 = 12x + 19 Reorder the terms: 7 + 7x + x2 = 19 + 12x Solving 7 + 7x + x2 = 19 + 12x Solving for variable 'x'. Reorder the terms: 7 + -19 + 7x + -12x + x2 = 19 + 12x + -19 + -12x Combine like terms: 7 + -19 = -12 -12 + 7x + -12x + x2 = 19 + 12x + -19 + -12x Combine like terms: 7x + -12x = -5x -12 + -5x + x2 = 19 + 12x + -19 + -12x Reorder the terms: -12 + -5x + x2 = 19 + -19 + 12x + -12x Combine like terms: 19 + -19 = 0 -12 + -5x + x2 = 0 + 12x + -12x -12 + -5x + x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -12 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -5x + x2 = 0 + 12 -5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -5x + x2 = 12 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 = 12 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 12 + 6.25 Combine like terms: 12 + 6.25 = 18.25 6.25 + -5x + x2 = 18.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + -2.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + -2.5 = 4.272001873 Simplifying x + -2.5 = 4.272001873 Reorder the terms: -2.5 + x = 4.272001873 Solving -2.5 + x = 4.272001873 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 = 4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.272001873 + 2.5 x = 4.272001873 + 2.5 Combine like terms: 4.272001873 + 2.5 = 6.772001873 x = 6.772001873 Simplifying x = 6.772001873Subproblem 2
x + -2.5 = -4.272001873 Simplifying x + -2.5 = -4.272001873 Reorder the terms: -2.5 + x = -4.272001873 Solving -2.5 + x = -4.272001873 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 = -4.272001873 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.272001873 + 2.5 x = -4.272001873 + 2.5 Combine like terms: -4.272001873 + 2.5 = -1.772001873 x = -1.772001873 Simplifying x = -1.772001873Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.772001873, -1.772001873}
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