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Simplifying x2 + 2 + -3 = 7x + 63 Reorder the terms: 2 + -3 + x2 = 7x + 63 Combine like terms: 2 + -3 = -1 -1 + x2 = 7x + 63 Reorder the terms: -1 + x2 = 63 + 7x Solving -1 + x2 = 63 + 7x Solving for variable 'x'. Reorder the terms: -1 + -63 + -7x + x2 = 63 + 7x + -63 + -7x Combine like terms: -1 + -63 = -64 -64 + -7x + x2 = 63 + 7x + -63 + -7x Reorder the terms: -64 + -7x + x2 = 63 + -63 + 7x + -7x Combine like terms: 63 + -63 = 0 -64 + -7x + x2 = 0 + 7x + -7x -64 + -7x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -64 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -7x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + -7x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -7x + x2 = 0 + 64 -7x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 -7x + x2 = 64 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 = 64 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 64 + 12.25 Combine like terms: 64 + 12.25 = 76.25 12.25 + -7x + x2 = 76.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (x + -3.5) equal to 8.732124598 and -8.732124598.Subproblem 1
x + -3.5 = 8.732124598 Simplifying x + -3.5 = 8.732124598 Reorder the terms: -3.5 + x = 8.732124598 Solving -3.5 + x = 8.732124598 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 = 8.732124598 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 8.732124598 + 3.5 x = 8.732124598 + 3.5 Combine like terms: 8.732124598 + 3.5 = 12.232124598 x = 12.232124598 Simplifying x = 12.232124598Subproblem 2
x + -3.5 = -8.732124598 Simplifying x + -3.5 = -8.732124598 Reorder the terms: -3.5 + x = -8.732124598 Solving -3.5 + x = -8.732124598 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 = -8.732124598 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -8.732124598 + 3.5 x = -8.732124598 + 3.5 Combine like terms: -8.732124598 + 3.5 = -5.232124598 x = -5.232124598 Simplifying x = -5.232124598Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.232124598, -5.232124598}
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