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Simplifying x2 + 10x + -290 = 0 Reorder the terms: -290 + 10x + x2 = 0 Solving -290 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '290' to each side of the equation. -290 + 10x + 290 + x2 = 0 + 290 Reorder the terms: -290 + 290 + 10x + x2 = 0 + 290 Combine like terms: -290 + 290 = 0 0 + 10x + x2 = 0 + 290 10x + x2 = 0 + 290 Combine like terms: 0 + 290 = 290 10x + x2 = 290 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 290 + 25 Reorder the terms: 25 + 10x + x2 = 290 + 25 Combine like terms: 290 + 25 = 315 25 + 10x + x2 = 315 Factor a perfect square on the left side: (x + 5)(x + 5) = 315 Calculate the square root of the right side: 17.748239349 Break this problem into two subproblems by setting (x + 5) equal to 17.748239349 and -17.748239349.Subproblem 1
x + 5 = 17.748239349 Simplifying x + 5 = 17.748239349 Reorder the terms: 5 + x = 17.748239349 Solving 5 + x = 17.748239349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 17.748239349 + -5 Combine like terms: 5 + -5 = 0 0 + x = 17.748239349 + -5 x = 17.748239349 + -5 Combine like terms: 17.748239349 + -5 = 12.748239349 x = 12.748239349 Simplifying x = 12.748239349Subproblem 2
x + 5 = -17.748239349 Simplifying x + 5 = -17.748239349 Reorder the terms: 5 + x = -17.748239349 Solving 5 + x = -17.748239349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -17.748239349 + -5 Combine like terms: 5 + -5 = 0 0 + x = -17.748239349 + -5 x = -17.748239349 + -5 Combine like terms: -17.748239349 + -5 = -22.748239349 x = -22.748239349 Simplifying x = -22.748239349Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.748239349, -22.748239349}
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