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Simplifying x2 + 70x + -25 = 0 Reorder the terms: -25 + 70x + x2 = 0 Solving -25 + 70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 70x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 70x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 70x + x2 = 0 + 25 70x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 70x + x2 = 25 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 = 25 + 1225 Reorder the terms: 1225 + 70x + x2 = 25 + 1225 Combine like terms: 25 + 1225 = 1250 1225 + 70x + x2 = 1250 Factor a perfect square on the left side: (x + 35)(x + 35) = 1250 Calculate the square root of the right side: 35.355339059 Break this problem into two subproblems by setting (x + 35) equal to 35.355339059 and -35.355339059.Subproblem 1
x + 35 = 35.355339059 Simplifying x + 35 = 35.355339059 Reorder the terms: 35 + x = 35.355339059 Solving 35 + x = 35.355339059 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 = 35.355339059 + -35 Combine like terms: 35 + -35 = 0 0 + x = 35.355339059 + -35 x = 35.355339059 + -35 Combine like terms: 35.355339059 + -35 = 0.355339059 x = 0.355339059 Simplifying x = 0.355339059Subproblem 2
x + 35 = -35.355339059 Simplifying x + 35 = -35.355339059 Reorder the terms: 35 + x = -35.355339059 Solving 35 + x = -35.355339059 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 = -35.355339059 + -35 Combine like terms: 35 + -35 = 0 0 + x = -35.355339059 + -35 x = -35.355339059 + -35 Combine like terms: -35.355339059 + -35 = -70.355339059 x = -70.355339059 Simplifying x = -70.355339059Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.355339059, -70.355339059}
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