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Simplifying 7x2 = 4x + 5 Reorder the terms: 7x2 = 5 + 4x Solving 7x2 = 5 + 4x Solving for variable 'x'. Reorder the terms: -5 + -4x + 7x2 = 5 + 4x + -5 + -4x Reorder the terms: -5 + -4x + 7x2 = 5 + -5 + 4x + -4x Combine like terms: 5 + -5 = 0 -5 + -4x + 7x2 = 0 + 4x + -4x -5 + -4x + 7x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -5 + -4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -0.5714285714x + 0.7142857143 + x2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -0.5714285714x + x2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + 0.7142857143 -0.5714285714x + x2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -0.5714285714x + x2 = 0.7142857143 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 0.7142857143 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 0.7142857143 + 0.08163265305 Combine like terms: 0.7142857143 + 0.08163265305 = 0.79591836735 0.08163265305 + -0.5714285714x + x2 = 0.79591836735 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 0.79591836735 Calculate the square root of the right side: 0.892142571 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 0.892142571 and -0.892142571.Subproblem 1
x + -0.2857142857 = 0.892142571 Simplifying x + -0.2857142857 = 0.892142571 Reorder the terms: -0.2857142857 + x = 0.892142571 Solving -0.2857142857 + x = 0.892142571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 0.892142571 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.892142571 + 0.2857142857 x = 0.892142571 + 0.2857142857 Combine like terms: 0.892142571 + 0.2857142857 = 1.1778568567 x = 1.1778568567 Simplifying x = 1.1778568567Subproblem 2
x + -0.2857142857 = -0.892142571 Simplifying x + -0.2857142857 = -0.892142571 Reorder the terms: -0.2857142857 + x = -0.892142571 Solving -0.2857142857 + x = -0.892142571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -0.892142571 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.892142571 + 0.2857142857 x = -0.892142571 + 0.2857142857 Combine like terms: -0.892142571 + 0.2857142857 = -0.6064282853 x = -0.6064282853 Simplifying x = -0.6064282853Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1778568567, -0.6064282853}
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