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Simplifying -28x2 + -32x + 16 = 0 Reorder the terms: 16 + -32x + -28x2 = 0 Solving 16 + -32x + -28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + -8x + -7x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + -8x + -7x2)' equal to zero and attempt to solve: Simplifying 4 + -8x + -7x2 = 0 Solving 4 + -8x + -7x2 = 0 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 = 0.3761785115 x = 0.3761785115 Simplifying x = 0.3761785115Subproblem 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 = -1.5190356545 x = -1.5190356545 Simplifying x = -1.5190356545Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3761785115, -1.5190356545}Solution
x = {0.3761785115, -1.5190356545}
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