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Simplifying x2 + (x + 7) = 65 Reorder the terms: x2 + (7 + x) = 65 Remove parenthesis around (7 + x) x2 + 7 + x = 65 Reorder the terms: 7 + x + x2 = 65 Solving 7 + x + x2 = 65 Solving for variable 'x'. Reorder the terms: 7 + -65 + x + x2 = 65 + -65 Combine like terms: 7 + -65 = -58 -58 + x + x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -58 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + x + x2 = 0 + 58 x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 x + x2 = 58 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 = 58 + 0.25 Reorder the terms: 0.25 + x + x2 = 58 + 0.25 Combine like terms: 58 + 0.25 = 58.25 0.25 + x + x2 = 58.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (x + 0.5) equal to 7.632168761 and -7.632168761.Subproblem 1
x + 0.5 = 7.632168761 Simplifying x + 0.5 = 7.632168761 Reorder the terms: 0.5 + x = 7.632168761 Solving 0.5 + x = 7.632168761 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 = 7.632168761 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.632168761 + -0.5 x = 7.632168761 + -0.5 Combine like terms: 7.632168761 + -0.5 = 7.132168761 x = 7.132168761 Simplifying x = 7.132168761Subproblem 2
x + 0.5 = -7.632168761 Simplifying x + 0.5 = -7.632168761 Reorder the terms: 0.5 + x = -7.632168761 Solving 0.5 + x = -7.632168761 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 = -7.632168761 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.632168761 + -0.5 x = -7.632168761 + -0.5 Combine like terms: -7.632168761 + -0.5 = -8.132168761 x = -8.132168761 Simplifying x = -8.132168761Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.132168761, -8.132168761}
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