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Simplifying x2 + 3 = x + 7 Reorder the terms: 3 + x2 = x + 7 Reorder the terms: 3 + x2 = 7 + x Solving 3 + x2 = 7 + x Solving for variable 'x'. Reorder the terms: 3 + -7 + -1x + x2 = 7 + x + -7 + -1x Combine like terms: 3 + -7 = -4 -4 + -1x + x2 = 7 + x + -7 + -1x Reorder the terms: -4 + -1x + x2 = 7 + -7 + x + -1x Combine like terms: 7 + -7 = 0 -4 + -1x + x2 = 0 + x + -1x -4 + -1x + x2 = x + -1x Combine like terms: x + -1x = 0 -4 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -1x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x + x2 = 0 + 4 -1x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1x + x2 = 4 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 4 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 4 + 0.25 Combine like terms: 4 + 0.25 = 4.25 0.25 + -1x + x2 = 4.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -0.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -0.5 = 2.061552813 Simplifying x + -0.5 = 2.061552813 Reorder the terms: -0.5 + x = 2.061552813 Solving -0.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.061552813 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.061552813 + 0.5 x = 2.061552813 + 0.5 Combine like terms: 2.061552813 + 0.5 = 2.561552813 x = 2.561552813 Simplifying x = 2.561552813Subproblem 2
x + -0.5 = -2.061552813 Simplifying x + -0.5 = -2.061552813 Reorder the terms: -0.5 + x = -2.061552813 Solving -0.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.061552813 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.061552813 + 0.5 x = -2.061552813 + 0.5 Combine like terms: -2.061552813 + 0.5 = -1.561552813 x = -1.561552813 Simplifying x = -1.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.561552813, -1.561552813}
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