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Simplifying x2 + 7x + -270 = 0 Reorder the terms: -270 + 7x + x2 = 0 Solving -270 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + 7x + 270 + x2 = 0 + 270 Reorder the terms: -270 + 270 + 7x + x2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + 7x + x2 = 0 + 270 7x + x2 = 0 + 270 Combine like terms: 0 + 270 = 270 7x + x2 = 270 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 = 270 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 270 + 12.25 Combine like terms: 270 + 12.25 = 282.25 12.25 + 7x + x2 = 282.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 282.25 Calculate the square root of the right side: 16.800297616 Break this problem into two subproblems by setting (x + 3.5) equal to 16.800297616 and -16.800297616.Subproblem 1
x + 3.5 = 16.800297616 Simplifying x + 3.5 = 16.800297616 Reorder the terms: 3.5 + x = 16.800297616 Solving 3.5 + x = 16.800297616 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 = 16.800297616 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 16.800297616 + -3.5 x = 16.800297616 + -3.5 Combine like terms: 16.800297616 + -3.5 = 13.300297616 x = 13.300297616 Simplifying x = 13.300297616Subproblem 2
x + 3.5 = -16.800297616 Simplifying x + 3.5 = -16.800297616 Reorder the terms: 3.5 + x = -16.800297616 Solving 3.5 + x = -16.800297616 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 = -16.800297616 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -16.800297616 + -3.5 x = -16.800297616 + -3.5 Combine like terms: -16.800297616 + -3.5 = -20.300297616 x = -20.300297616 Simplifying x = -20.300297616Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.300297616, -20.300297616}
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