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Simplifying x2 + x + -465 = 0 Reorder the terms: -465 + x + x2 = 0 Solving -465 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '465' to each side of the equation. -465 + x + 465 + x2 = 0 + 465 Reorder the terms: -465 + 465 + x + x2 = 0 + 465 Combine like terms: -465 + 465 = 0 0 + x + x2 = 0 + 465 x + x2 = 0 + 465 Combine like terms: 0 + 465 = 465 x + x2 = 465 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 = 465 + 0.25 Reorder the terms: 0.25 + x + x2 = 465 + 0.25 Combine like terms: 465 + 0.25 = 465.25 0.25 + x + x2 = 465.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 465.25 Calculate the square root of the right side: 21.56965461 Break this problem into two subproblems by setting (x + 0.5) equal to 21.56965461 and -21.56965461.Subproblem 1
x + 0.5 = 21.56965461 Simplifying x + 0.5 = 21.56965461 Reorder the terms: 0.5 + x = 21.56965461 Solving 0.5 + x = 21.56965461 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 = 21.56965461 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 21.56965461 + -0.5 x = 21.56965461 + -0.5 Combine like terms: 21.56965461 + -0.5 = 21.06965461 x = 21.06965461 Simplifying x = 21.06965461Subproblem 2
x + 0.5 = -21.56965461 Simplifying x + 0.5 = -21.56965461 Reorder the terms: 0.5 + x = -21.56965461 Solving 0.5 + x = -21.56965461 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 = -21.56965461 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -21.56965461 + -0.5 x = -21.56965461 + -0.5 Combine like terms: -21.56965461 + -0.5 = -22.06965461 x = -22.06965461 Simplifying x = -22.06965461Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.06965461, -22.06965461}
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