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Simplifying 7x2 = 5x + 10 Reorder the terms: 7x2 = 10 + 5x Solving 7x2 = 10 + 5x Solving for variable 'x'. Reorder the terms: -10 + -5x + 7x2 = 10 + 5x + -10 + -5x Reorder the terms: -10 + -5x + 7x2 = 10 + -10 + 5x + -5x Combine like terms: 10 + -10 = 0 -10 + -5x + 7x2 = 0 + 5x + -5x -10 + -5x + 7x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -10 + -5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.428571429 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -0.7142857143x + 1.428571429 + x2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -0.7142857143x + x2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -0.7142857143x + x2 = 0 + 1.428571429 -0.7142857143x + x2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -0.7142857143x + x2 = 1.428571429 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 1.428571429 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 1.428571429 + 0.1275510204 Combine like terms: 1.428571429 + 0.1275510204 = 1.5561224494 0.1275510204 + -0.7142857143x + x2 = 1.5561224494 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 1.5561224494 Calculate the square root of the right side: 1.247446371 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 1.247446371 and -1.247446371.Subproblem 1
x + -0.3571428572 = 1.247446371 Simplifying x + -0.3571428572 = 1.247446371 Reorder the terms: -0.3571428572 + x = 1.247446371 Solving -0.3571428572 + x = 1.247446371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 1.247446371 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 1.247446371 + 0.3571428572 x = 1.247446371 + 0.3571428572 Combine like terms: 1.247446371 + 0.3571428572 = 1.6045892282 x = 1.6045892282 Simplifying x = 1.6045892282Subproblem 2
x + -0.3571428572 = -1.247446371 Simplifying x + -0.3571428572 = -1.247446371 Reorder the terms: -0.3571428572 + x = -1.247446371 Solving -0.3571428572 + x = -1.247446371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -1.247446371 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -1.247446371 + 0.3571428572 x = -1.247446371 + 0.3571428572 Combine like terms: -1.247446371 + 0.3571428572 = -0.8903035138 x = -0.8903035138 Simplifying x = -0.8903035138Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6045892282, -0.8903035138}
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