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Simplifying x2 + x + 8 = 78 Reorder the terms: 8 + x + x2 = 78 Solving 8 + x + x2 = 78 Solving for variable 'x'. Reorder the terms: 8 + -78 + x + x2 = 78 + -78 Combine like terms: 8 + -78 = -70 -70 + x + x2 = 78 + -78 Combine like terms: 78 + -78 = 0 -70 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + x + x2 = 0 + 70 x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 x + x2 = 70 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 = 70 + 0.25 Reorder the terms: 0.25 + x + x2 = 70 + 0.25 Combine like terms: 70 + 0.25 = 70.25 0.25 + x + x2 = 70.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (x + 0.5) equal to 8.381527307 and -8.381527307.Subproblem 1
x + 0.5 = 8.381527307 Simplifying x + 0.5 = 8.381527307 Reorder the terms: 0.5 + x = 8.381527307 Solving 0.5 + x = 8.381527307 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 = 8.381527307 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.381527307 + -0.5 x = 8.381527307 + -0.5 Combine like terms: 8.381527307 + -0.5 = 7.881527307 x = 7.881527307 Simplifying x = 7.881527307Subproblem 2
x + 0.5 = -8.381527307 Simplifying x + 0.5 = -8.381527307 Reorder the terms: 0.5 + x = -8.381527307 Solving 0.5 + x = -8.381527307 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 = -8.381527307 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.381527307 + -0.5 x = -8.381527307 + -0.5 Combine like terms: -8.381527307 + -0.5 = -8.881527307 x = -8.881527307 Simplifying x = -8.881527307Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.881527307, -8.881527307}
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