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Simplifying x2 + 10x + -85 = 0 Reorder the terms: -85 + 10x + x2 = 0 Solving -85 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + 10x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + 10x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + 10x + x2 = 0 + 85 10x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 10x + x2 = 85 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 = 85 + 25 Reorder the terms: 25 + 10x + x2 = 85 + 25 Combine like terms: 85 + 25 = 110 25 + 10x + x2 = 110 Factor a perfect square on the left side: (x + 5)(x + 5) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (x + 5) equal to 10.488088482 and -10.488088482.Subproblem 1
x + 5 = 10.488088482 Simplifying x + 5 = 10.488088482 Reorder the terms: 5 + x = 10.488088482 Solving 5 + x = 10.488088482 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 = 10.488088482 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.488088482 + -5 x = 10.488088482 + -5 Combine like terms: 10.488088482 + -5 = 5.488088482 x = 5.488088482 Simplifying x = 5.488088482Subproblem 2
x + 5 = -10.488088482 Simplifying x + 5 = -10.488088482 Reorder the terms: 5 + x = -10.488088482 Solving 5 + x = -10.488088482 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 = -10.488088482 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.488088482 + -5 x = -10.488088482 + -5 Combine like terms: -10.488088482 + -5 = -15.488088482 x = -15.488088482 Simplifying x = -15.488088482Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.488088482, -15.488088482}
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