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Simplifying x * x + -1x = 465 Multiply x * x x2 + -1x = 465 Reorder the terms: -1x + x2 = 465 Solving -1x + x2 = 465 Solving for variable 'x'. Reorder the terms: -465 + -1x + x2 = 465 + -465 Combine like terms: 465 + -465 = 0 -465 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '465' to each side of the equation. -465 + -1x + 465 + x2 = 0 + 465 Reorder the terms: -465 + 465 + -1x + x2 = 0 + 465 Combine like terms: -465 + 465 = 0 0 + -1x + x2 = 0 + 465 -1x + x2 = 0 + 465 Combine like terms: 0 + 465 = 465 -1x + x2 = 465 The x term is -1x. 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. -1x + 0.25 + x2 = 465 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 465 + 0.25 Combine like terms: 465 + 0.25 = 465.25 0.25 + -1x + 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 = 22.06965461 x = 22.06965461 Simplifying x = 22.06965461Subproblem 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 = -21.06965461 x = -21.06965461 Simplifying x = -21.06965461Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.06965461, -21.06965461}
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