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Simplifying x2 + 15x + -7 = 12x + 8 Reorder the terms: -7 + 15x + x2 = 12x + 8 Reorder the terms: -7 + 15x + x2 = 8 + 12x Solving -7 + 15x + x2 = 8 + 12x Solving for variable 'x'. Reorder the terms: -7 + -8 + 15x + -12x + x2 = 8 + 12x + -8 + -12x Combine like terms: -7 + -8 = -15 -15 + 15x + -12x + x2 = 8 + 12x + -8 + -12x Combine like terms: 15x + -12x = 3x -15 + 3x + x2 = 8 + 12x + -8 + -12x Reorder the terms: -15 + 3x + x2 = 8 + -8 + 12x + -12x Combine like terms: 8 + -8 = 0 -15 + 3x + x2 = 0 + 12x + -12x -15 + 3x + x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -15 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 3x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 3x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 3x + x2 = 0 + 15 3x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 3x + x2 = 15 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 15 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 15 + 2.25 Combine like terms: 15 + 2.25 = 17.25 2.25 + 3x + x2 = 17.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + 1.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + 1.5 = 4.153311931 Simplifying x + 1.5 = 4.153311931 Reorder the terms: 1.5 + x = 4.153311931 Solving 1.5 + x = 4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 4.153311931 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.153311931 + -1.5 x = 4.153311931 + -1.5 Combine like terms: 4.153311931 + -1.5 = 2.653311931 x = 2.653311931 Simplifying x = 2.653311931Subproblem 2
x + 1.5 = -4.153311931 Simplifying x + 1.5 = -4.153311931 Reorder the terms: 1.5 + x = -4.153311931 Solving 1.5 + x = -4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -4.153311931 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.153311931 + -1.5 x = -4.153311931 + -1.5 Combine like terms: -4.153311931 + -1.5 = -5.653311931 x = -5.653311931 Simplifying x = -5.653311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.653311931, -5.653311931}
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