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Simplifying x2 + 10x + -1035 = 0 Reorder the terms: -1035 + 10x + x2 = 0 Solving -1035 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1035' to each side of the equation. -1035 + 10x + 1035 + x2 = 0 + 1035 Reorder the terms: -1035 + 1035 + 10x + x2 = 0 + 1035 Combine like terms: -1035 + 1035 = 0 0 + 10x + x2 = 0 + 1035 10x + x2 = 0 + 1035 Combine like terms: 0 + 1035 = 1035 10x + x2 = 1035 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 = 1035 + 25 Reorder the terms: 25 + 10x + x2 = 1035 + 25 Combine like terms: 1035 + 25 = 1060 25 + 10x + x2 = 1060 Factor a perfect square on the left side: (x + 5)(x + 5) = 1060 Calculate the square root of the right side: 32.557641192 Break this problem into two subproblems by setting (x + 5) equal to 32.557641192 and -32.557641192.Subproblem 1
x + 5 = 32.557641192 Simplifying x + 5 = 32.557641192 Reorder the terms: 5 + x = 32.557641192 Solving 5 + x = 32.557641192 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 = 32.557641192 + -5 Combine like terms: 5 + -5 = 0 0 + x = 32.557641192 + -5 x = 32.557641192 + -5 Combine like terms: 32.557641192 + -5 = 27.557641192 x = 27.557641192 Simplifying x = 27.557641192Subproblem 2
x + 5 = -32.557641192 Simplifying x + 5 = -32.557641192 Reorder the terms: 5 + x = -32.557641192 Solving 5 + x = -32.557641192 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 = -32.557641192 + -5 Combine like terms: 5 + -5 = 0 0 + x = -32.557641192 + -5 x = -32.557641192 + -5 Combine like terms: -32.557641192 + -5 = -37.557641192 x = -37.557641192 Simplifying x = -37.557641192Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.557641192, -37.557641192}
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