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Simplifying x2 + 70x + -210 = 0 Reorder the terms: -210 + 70x + x2 = 0 Solving -210 + 70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '210' to each side of the equation. -210 + 70x + 210 + x2 = 0 + 210 Reorder the terms: -210 + 210 + 70x + x2 = 0 + 210 Combine like terms: -210 + 210 = 0 0 + 70x + x2 = 0 + 210 70x + x2 = 0 + 210 Combine like terms: 0 + 210 = 210 70x + x2 = 210 The x term is 70x. Take half its coefficient (35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. 70x + 1225 + x2 = 210 + 1225 Reorder the terms: 1225 + 70x + x2 = 210 + 1225 Combine like terms: 210 + 1225 = 1435 1225 + 70x + x2 = 1435 Factor a perfect square on the left side: (x + 35)(x + 35) = 1435 Calculate the square root of the right side: 37.88139385 Break this problem into two subproblems by setting (x + 35) equal to 37.88139385 and -37.88139385.Subproblem 1
x + 35 = 37.88139385 Simplifying x + 35 = 37.88139385 Reorder the terms: 35 + x = 37.88139385 Solving 35 + x = 37.88139385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = 37.88139385 + -35 Combine like terms: 35 + -35 = 0 0 + x = 37.88139385 + -35 x = 37.88139385 + -35 Combine like terms: 37.88139385 + -35 = 2.88139385 x = 2.88139385 Simplifying x = 2.88139385Subproblem 2
x + 35 = -37.88139385 Simplifying x + 35 = -37.88139385 Reorder the terms: 35 + x = -37.88139385 Solving 35 + x = -37.88139385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + x = -37.88139385 + -35 Combine like terms: 35 + -35 = 0 0 + x = -37.88139385 + -35 x = -37.88139385 + -35 Combine like terms: -37.88139385 + -35 = -72.88139385 x = -72.88139385 Simplifying x = -72.88139385Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.88139385, -72.88139385}
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