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Simplifying 0.1x2 + 70x + 900 = 0 Reorder the terms: 900 + 70x + 0.1x2 = 0 Solving 900 + 70x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 9000 + 700x + x2 = 0 Move the constant term to the right: Add '-9000' to each side of the equation. 9000 + 700x + -9000 + x2 = 0 + -9000 Reorder the terms: 9000 + -9000 + 700x + x2 = 0 + -9000 Combine like terms: 9000 + -9000 = 0 0 + 700x + x2 = 0 + -9000 700x + x2 = 0 + -9000 Combine like terms: 0 + -9000 = -9000 700x + x2 = -9000 The x term is 700x. Take half its coefficient (350). Square it (122500) and add it to both sides. Add '122500' to each side of the equation. 700x + 122500 + x2 = -9000 + 122500 Reorder the terms: 122500 + 700x + x2 = -9000 + 122500 Combine like terms: -9000 + 122500 = 113500 122500 + 700x + x2 = 113500 Factor a perfect square on the left side: (x + 350)(x + 350) = 113500 Calculate the square root of the right side: 336.897610558 Break this problem into two subproblems by setting (x + 350) equal to 336.897610558 and -336.897610558.Subproblem 1
x + 350 = 336.897610558 Simplifying x + 350 = 336.897610558 Reorder the terms: 350 + x = 336.897610558 Solving 350 + x = 336.897610558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + x = 336.897610558 + -350 Combine like terms: 350 + -350 = 0 0 + x = 336.897610558 + -350 x = 336.897610558 + -350 Combine like terms: 336.897610558 + -350 = -13.102389442 x = -13.102389442 Simplifying x = -13.102389442Subproblem 2
x + 350 = -336.897610558 Simplifying x + 350 = -336.897610558 Reorder the terms: 350 + x = -336.897610558 Solving 350 + x = -336.897610558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-350' to each side of the equation. 350 + -350 + x = -336.897610558 + -350 Combine like terms: 350 + -350 = 0 0 + x = -336.897610558 + -350 x = -336.897610558 + -350 Combine like terms: -336.897610558 + -350 = -686.897610558 x = -686.897610558 Simplifying x = -686.897610558Solution
The solution to the problem is based on the solutions from the subproblems. x = {-13.102389442, -686.897610558}
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