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Simplifying 8 = x2 + -7x + 3 Reorder the terms: 8 = 3 + -7x + x2 Solving 8 = 3 + -7x + x2 Solving for variable 'x'. Combine like terms: 8 + -3 = 5 5 + 7x + -1x2 = 3 + -7x + x2 + -3 + 7x + -1x2 Reorder the terms: 5 + 7x + -1x2 = 3 + -3 + -7x + 7x + x2 + -1x2 Combine like terms: 3 + -3 = 0 5 + 7x + -1x2 = 0 + -7x + 7x + x2 + -1x2 5 + 7x + -1x2 = -7x + 7x + x2 + -1x2 Combine like terms: -7x + 7x = 0 5 + 7x + -1x2 = 0 + x2 + -1x2 5 + 7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -7x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -7x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -7x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7x + x2 = 0 + 5 -7x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -7x + x2 = 5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 5 + 12.25 Combine like terms: 5 + 12.25 = 17.25 12.25 + -7x + x2 = 17.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + -3.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + -3.5 = 4.153311931 Simplifying x + -3.5 = 4.153311931 Reorder the terms: -3.5 + x = 4.153311931 Solving -3.5 + x = 4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.153311931 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.153311931 + 3.5 x = 4.153311931 + 3.5 Combine like terms: 4.153311931 + 3.5 = 7.653311931 x = 7.653311931 Simplifying x = 7.653311931Subproblem 2
x + -3.5 = -4.153311931 Simplifying x + -3.5 = -4.153311931 Reorder the terms: -3.5 + x = -4.153311931 Solving -3.5 + x = -4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.153311931 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.153311931 + 3.5 x = -4.153311931 + 3.5 Combine like terms: -4.153311931 + 3.5 = -0.653311931 x = -0.653311931 Simplifying x = -0.653311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.653311931, -0.653311931}
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