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Simplifying x2 + x = 76 Reorder the terms: x + x2 = 76 Solving x + x2 = 76 Solving for variable 'x'. Reorder the terms: -76 + x + x2 = 76 + -76 Combine like terms: 76 + -76 = 0 -76 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + x + x2 = 0 + 76 x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 x + x2 = 76 The x term is x. 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. x + 0.25 + x2 = 76 + 0.25 Reorder the terms: 0.25 + x + x2 = 76 + 0.25 Combine like terms: 76 + 0.25 = 76.25 0.25 + x + x2 = 76.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (x + 0.5) equal to 8.732124598 and -8.732124598.Subproblem 1
x + 0.5 = 8.732124598 Simplifying x + 0.5 = 8.732124598 Reorder the terms: 0.5 + x = 8.732124598 Solving 0.5 + x = 8.732124598 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 = 8.732124598 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.732124598 + -0.5 x = 8.732124598 + -0.5 Combine like terms: 8.732124598 + -0.5 = 8.232124598 x = 8.232124598 Simplifying x = 8.232124598Subproblem 2
x + 0.5 = -8.732124598 Simplifying x + 0.5 = -8.732124598 Reorder the terms: 0.5 + x = -8.732124598 Solving 0.5 + x = -8.732124598 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 = -8.732124598 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.732124598 + -0.5 x = -8.732124598 + -0.5 Combine like terms: -8.732124598 + -0.5 = -9.232124598 x = -9.232124598 Simplifying x = -9.232124598Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.232124598, -9.232124598}
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