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Simplifying 60 + 70x + -1x2 = 0 Solving 60 + 70x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -60 + -70x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -70x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -70x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -70x + x2 = 0 + 60 -70x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -70x + x2 = 60 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 = 60 + 1225 Reorder the terms: 1225 + -70x + x2 = 60 + 1225 Combine like terms: 60 + 1225 = 1285 1225 + -70x + x2 = 1285 Factor a perfect square on the left side: (x + -35)(x + -35) = 1285 Calculate the square root of the right side: 35.846896658 Break this problem into two subproblems by setting (x + -35) equal to 35.846896658 and -35.846896658.Subproblem 1
x + -35 = 35.846896658 Simplifying x + -35 = 35.846896658 Reorder the terms: -35 + x = 35.846896658 Solving -35 + x = 35.846896658 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 = 35.846896658 + 35 Combine like terms: -35 + 35 = 0 0 + x = 35.846896658 + 35 x = 35.846896658 + 35 Combine like terms: 35.846896658 + 35 = 70.846896658 x = 70.846896658 Simplifying x = 70.846896658Subproblem 2
x + -35 = -35.846896658 Simplifying x + -35 = -35.846896658 Reorder the terms: -35 + x = -35.846896658 Solving -35 + x = -35.846896658 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 = -35.846896658 + 35 Combine like terms: -35 + 35 = 0 0 + x = -35.846896658 + 35 x = -35.846896658 + 35 Combine like terms: -35.846896658 + 35 = -0.846896658 x = -0.846896658 Simplifying x = -0.846896658Solution
The solution to the problem is based on the solutions from the subproblems. x = {70.846896658, -0.846896658}
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