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Simplifying 7x2 = 5x + 3 Reorder the terms: 7x2 = 3 + 5x Solving 7x2 = 3 + 5x Solving for variable 'x'. Reorder the terms: -3 + -5x + 7x2 = 3 + 5x + -3 + -5x Reorder the terms: -3 + -5x + 7x2 = 3 + -3 + 5x + -5x Combine like terms: 3 + -3 = 0 -3 + -5x + 7x2 = 0 + 5x + -5x -3 + -5x + 7x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -3 + -5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.4285714286 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.7142857143x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.7142857143x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.7142857143x + x2 = 0 + 0.4285714286 -0.7142857143x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.7142857143x + x2 = 0.4285714286 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 = 0.4285714286 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 0.4285714286 + 0.1275510204 Combine like terms: 0.4285714286 + 0.1275510204 = 0.556122449 0.1275510204 + -0.7142857143x + x2 = 0.556122449 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 0.556122449 Calculate the square root of the right side: 0.745736179 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 0.745736179 and -0.745736179.Subproblem 1
x + -0.3571428572 = 0.745736179 Simplifying x + -0.3571428572 = 0.745736179 Reorder the terms: -0.3571428572 + x = 0.745736179 Solving -0.3571428572 + x = 0.745736179 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 = 0.745736179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 0.745736179 + 0.3571428572 x = 0.745736179 + 0.3571428572 Combine like terms: 0.745736179 + 0.3571428572 = 1.1028790362 x = 1.1028790362 Simplifying x = 1.1028790362Subproblem 2
x + -0.3571428572 = -0.745736179 Simplifying x + -0.3571428572 = -0.745736179 Reorder the terms: -0.3571428572 + x = -0.745736179 Solving -0.3571428572 + x = -0.745736179 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 = -0.745736179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -0.745736179 + 0.3571428572 x = -0.745736179 + 0.3571428572 Combine like terms: -0.745736179 + 0.3571428572 = -0.3885933218 x = -0.3885933218 Simplifying x = -0.3885933218Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1028790362, -0.3885933218}
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