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Simplifying -7x2 + 8x + 4 = 0 Reorder the terms: 4 + 8x + -7x2 = 0 Solving 4 + 8x + -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'. -0.5714285714 + -1.142857143x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + -1.142857143x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + -1.142857143x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + -1.142857143x + x2 = 0 + 0.5714285714 -1.142857143x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 -1.142857143x + x2 = 0.5714285714 The x term is -1.142857143x. Take half its coefficient (-0.5714285715). Square it (0.3265306123) and add it to both sides. Add '0.3265306123' to each side of the equation. -1.142857143x + 0.3265306123 + x2 = 0.5714285714 + 0.3265306123 Reorder the terms: 0.3265306123 + -1.142857143x + x2 = 0.5714285714 + 0.3265306123 Combine like terms: 0.5714285714 + 0.3265306123 = 0.8979591837 0.3265306123 + -1.142857143x + x2 = 0.8979591837 Factor a perfect square on the left side: (x + -0.5714285715)(x + -0.5714285715) = 0.8979591837 Calculate the square root of the right side: 0.947607083 Break this problem into two subproblems by setting (x + -0.5714285715) equal to 0.947607083 and -0.947607083.Subproblem 1
x + -0.5714285715 = 0.947607083 Simplifying x + -0.5714285715 = 0.947607083 Reorder the terms: -0.5714285715 + x = 0.947607083 Solving -0.5714285715 + x = 0.947607083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = 0.947607083 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = 0.947607083 + 0.5714285715 x = 0.947607083 + 0.5714285715 Combine like terms: 0.947607083 + 0.5714285715 = 1.5190356545 x = 1.5190356545 Simplifying x = 1.5190356545Subproblem 2
x + -0.5714285715 = -0.947607083 Simplifying x + -0.5714285715 = -0.947607083 Reorder the terms: -0.5714285715 + x = -0.947607083 Solving -0.5714285715 + x = -0.947607083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + x = -0.947607083 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + x = -0.947607083 + 0.5714285715 x = -0.947607083 + 0.5714285715 Combine like terms: -0.947607083 + 0.5714285715 = -0.3761785115 x = -0.3761785115 Simplifying x = -0.3761785115Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5190356545, -0.3761785115}
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