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Simplifying 7x2 + 4x + -28 = 0 Reorder the terms: -28 + 4x + 7x2 = 0 Solving -28 + 4x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.5714285714x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.5714285714x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.5714285714x + x2 = 0 + 4 0.5714285714x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.5714285714x + x2 = 4 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 = 4 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 4 + 0.08163265305 Combine like terms: 4 + 0.08163265305 = 4.08163265305 0.08163265305 + 0.5714285714x + x2 = 4.08163265305 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 4.08163265305 Calculate the square root of the right side: 2.020305089 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 2.020305089 and -2.020305089.Subproblem 1
x + 0.2857142857 = 2.020305089 Simplifying x + 0.2857142857 = 2.020305089 Reorder the terms: 0.2857142857 + x = 2.020305089 Solving 0.2857142857 + x = 2.020305089 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 = 2.020305089 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 2.020305089 + -0.2857142857 x = 2.020305089 + -0.2857142857 Combine like terms: 2.020305089 + -0.2857142857 = 1.7345908033 x = 1.7345908033 Simplifying x = 1.7345908033Subproblem 2
x + 0.2857142857 = -2.020305089 Simplifying x + 0.2857142857 = -2.020305089 Reorder the terms: 0.2857142857 + x = -2.020305089 Solving 0.2857142857 + x = -2.020305089 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 = -2.020305089 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -2.020305089 + -0.2857142857 x = -2.020305089 + -0.2857142857 Combine like terms: -2.020305089 + -0.2857142857 = -2.3060193747 x = -2.3060193747 Simplifying x = -2.3060193747Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7345908033, -2.3060193747}
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