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Simplifying 2x2 = 7 + -20x Solving 2x2 = 7 + -20x Solving for variable 'x'. Reorder the terms: -7 + 20x + 2x2 = 7 + -20x + -7 + 20x Reorder the terms: -7 + 20x + 2x2 = 7 + -7 + -20x + 20x Combine like terms: 7 + -7 = 0 -7 + 20x + 2x2 = 0 + -20x + 20x -7 + 20x + 2x2 = -20x + 20x Combine like terms: -20x + 20x = 0 -7 + 20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 10x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 10x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 10x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 10x + x2 = 0 + 3.5 10x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 10x + x2 = 3.5 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 3.5 + 25 Reorder the terms: 25 + 10x + x2 = 3.5 + 25 Combine like terms: 3.5 + 25 = 28.5 25 + 10x + x2 = 28.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 28.5 Calculate the square root of the right side: 5.338539126 Break this problem into two subproblems by setting (x + 5) equal to 5.338539126 and -5.338539126.Subproblem 1
x + 5 = 5.338539126 Simplifying x + 5 = 5.338539126 Reorder the terms: 5 + x = 5.338539126 Solving 5 + x = 5.338539126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.338539126 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.338539126 + -5 x = 5.338539126 + -5 Combine like terms: 5.338539126 + -5 = 0.338539126 x = 0.338539126 Simplifying x = 0.338539126Subproblem 2
x + 5 = -5.338539126 Simplifying x + 5 = -5.338539126 Reorder the terms: 5 + x = -5.338539126 Solving 5 + x = -5.338539126 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.338539126 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.338539126 + -5 x = -5.338539126 + -5 Combine like terms: -5.338539126 + -5 = -10.338539126 x = -10.338539126 Simplifying x = -10.338539126Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.338539126, -10.338539126}
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