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Simplifying x2 + 70x + 385 = 0 Reorder the terms: 385 + 70x + x2 = 0 Solving 385 + 70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-385' to each side of the equation. 385 + 70x + -385 + x2 = 0 + -385 Reorder the terms: 385 + -385 + 70x + x2 = 0 + -385 Combine like terms: 385 + -385 = 0 0 + 70x + x2 = 0 + -385 70x + x2 = 0 + -385 Combine like terms: 0 + -385 = -385 70x + x2 = -385 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 = -385 + 1225 Reorder the terms: 1225 + 70x + x2 = -385 + 1225 Combine like terms: -385 + 1225 = 840 1225 + 70x + x2 = 840 Factor a perfect square on the left side: (x + 35)(x + 35) = 840 Calculate the square root of the right side: 28.982753492 Break this problem into two subproblems by setting (x + 35) equal to 28.982753492 and -28.982753492.Subproblem 1
x + 35 = 28.982753492 Simplifying x + 35 = 28.982753492 Reorder the terms: 35 + x = 28.982753492 Solving 35 + x = 28.982753492 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 = 28.982753492 + -35 Combine like terms: 35 + -35 = 0 0 + x = 28.982753492 + -35 x = 28.982753492 + -35 Combine like terms: 28.982753492 + -35 = -6.017246508 x = -6.017246508 Simplifying x = -6.017246508Subproblem 2
x + 35 = -28.982753492 Simplifying x + 35 = -28.982753492 Reorder the terms: 35 + x = -28.982753492 Solving 35 + x = -28.982753492 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 = -28.982753492 + -35 Combine like terms: 35 + -35 = 0 0 + x = -28.982753492 + -35 x = -28.982753492 + -35 Combine like terms: -28.982753492 + -35 = -63.982753492 x = -63.982753492 Simplifying x = -63.982753492Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.017246508, -63.982753492}
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