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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 = 70.355339059 x = 70.355339059 Simplifying x = 70.355339059Subproblem 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 = -0.355339059 x = -0.355339059 Simplifying x = -0.355339059Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.355339059, -0.355339059}
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