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Simplifying x * x + -7x + -961 = 0 Multiply x * x x2 + -7x + -961 = 0 Reorder the terms: -961 + -7x + x2 = 0 Solving -961 + -7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '961' to each side of the equation. -961 + -7x + 961 + x2 = 0 + 961 Reorder the terms: -961 + 961 + -7x + x2 = 0 + 961 Combine like terms: -961 + 961 = 0 0 + -7x + x2 = 0 + 961 -7x + x2 = 0 + 961 Combine like terms: 0 + 961 = 961 -7x + x2 = 961 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 961 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 961 + 12.25 Combine like terms: 961 + 12.25 = 973.25 12.25 + -7x + x2 = 973.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 973.25 Calculate the square root of the right side: 31.19695498 Break this problem into two subproblems by setting (x + -3.5) equal to 31.19695498 and -31.19695498.Subproblem 1
x + -3.5 = 31.19695498 Simplifying x + -3.5 = 31.19695498 Reorder the terms: -3.5 + x = 31.19695498 Solving -3.5 + x = 31.19695498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 31.19695498 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 31.19695498 + 3.5 x = 31.19695498 + 3.5 Combine like terms: 31.19695498 + 3.5 = 34.69695498 x = 34.69695498 Simplifying x = 34.69695498Subproblem 2
x + -3.5 = -31.19695498 Simplifying x + -3.5 = -31.19695498 Reorder the terms: -3.5 + x = -31.19695498 Solving -3.5 + x = -31.19695498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -31.19695498 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -31.19695498 + 3.5 x = -31.19695498 + 3.5 Combine like terms: -31.19695498 + 3.5 = -27.69695498 x = -27.69695498 Simplifying x = -27.69695498Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.69695498, -27.69695498}
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