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Simplifying 10x2 = 220 + -7x Solving 10x2 = 220 + -7x Solving for variable 'x'. Reorder the terms: -220 + 7x + 10x2 = 220 + -7x + -220 + 7x Reorder the terms: -220 + 7x + 10x2 = 220 + -220 + -7x + 7x Combine like terms: 220 + -220 = 0 -220 + 7x + 10x2 = 0 + -7x + 7x -220 + 7x + 10x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -220 + 7x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -22 + 0.7x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + 0.7x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 0.7x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 0.7x + x2 = 0 + 22 0.7x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 0.7x + x2 = 22 The x term is 0.7x. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7x + 0.1225 + x2 = 22 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = 22 + 0.1225 Combine like terms: 22 + 0.1225 = 22.1225 0.1225 + 0.7x + x2 = 22.1225 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = 22.1225 Calculate the square root of the right side: 4.703456176 Break this problem into two subproblems by setting (x + 0.35) equal to 4.703456176 and -4.703456176.Subproblem 1
x + 0.35 = 4.703456176 Simplifying x + 0.35 = 4.703456176 Reorder the terms: 0.35 + x = 4.703456176 Solving 0.35 + x = 4.703456176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = 4.703456176 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = 4.703456176 + -0.35 x = 4.703456176 + -0.35 Combine like terms: 4.703456176 + -0.35 = 4.353456176 x = 4.353456176 Simplifying x = 4.353456176Subproblem 2
x + 0.35 = -4.703456176 Simplifying x + 0.35 = -4.703456176 Reorder the terms: 0.35 + x = -4.703456176 Solving 0.35 + x = -4.703456176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.35' to each side of the equation. 0.35 + -0.35 + x = -4.703456176 + -0.35 Combine like terms: 0.35 + -0.35 = 0.00 0.00 + x = -4.703456176 + -0.35 x = -4.703456176 + -0.35 Combine like terms: -4.703456176 + -0.35 = -5.053456176 x = -5.053456176 Simplifying x = -5.053456176Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.353456176, -5.053456176}
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