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Simplifying 28x2 + -96x + -144 = 0 Reorder the terms: -144 + -96x + 28x2 = 0 Solving -144 + -96x + 28x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-36 + -24x + 7x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-36 + -24x + 7x2)' equal to zero and attempt to solve: Simplifying -36 + -24x + 7x2 = 0 Solving -36 + -24x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -5.142857143 + -3.428571429x + x2 = 0 Move the constant term to the right: Add '5.142857143' to each side of the equation. -5.142857143 + -3.428571429x + 5.142857143 + x2 = 0 + 5.142857143 Reorder the terms: -5.142857143 + 5.142857143 + -3.428571429x + x2 = 0 + 5.142857143 Combine like terms: -5.142857143 + 5.142857143 = 0.000000000 0.000000000 + -3.428571429x + x2 = 0 + 5.142857143 -3.428571429x + x2 = 0 + 5.142857143 Combine like terms: 0 + 5.142857143 = 5.142857143 -3.428571429x + x2 = 5.142857143 The x term is -3.428571429x. Take half its coefficient (-1.714285715). Square it (2.938775513) and add it to both sides. Add '2.938775513' to each side of the equation. -3.428571429x + 2.938775513 + x2 = 5.142857143 + 2.938775513 Reorder the terms: 2.938775513 + -3.428571429x + x2 = 5.142857143 + 2.938775513 Combine like terms: 5.142857143 + 2.938775513 = 8.081632656 2.938775513 + -3.428571429x + x2 = 8.081632656 Factor a perfect square on the left side: (x + -1.714285715)(x + -1.714285715) = 8.081632656 Calculate the square root of the right side: 2.842821249 Break this problem into two subproblems by setting (x + -1.714285715) equal to 2.842821249 and -2.842821249.Subproblem 1
x + -1.714285715 = 2.842821249 Simplifying x + -1.714285715 = 2.842821249 Reorder the terms: -1.714285715 + x = 2.842821249 Solving -1.714285715 + x = 2.842821249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + x = 2.842821249 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + x = 2.842821249 + 1.714285715 x = 2.842821249 + 1.714285715 Combine like terms: 2.842821249 + 1.714285715 = 4.557106964 x = 4.557106964 Simplifying x = 4.557106964Subproblem 2
x + -1.714285715 = -2.842821249 Simplifying x + -1.714285715 = -2.842821249 Reorder the terms: -1.714285715 + x = -2.842821249 Solving -1.714285715 + x = -2.842821249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.714285715' to each side of the equation. -1.714285715 + 1.714285715 + x = -2.842821249 + 1.714285715 Combine like terms: -1.714285715 + 1.714285715 = 0.000000000 0.000000000 + x = -2.842821249 + 1.714285715 x = -2.842821249 + 1.714285715 Combine like terms: -2.842821249 + 1.714285715 = -1.128535534 x = -1.128535534 Simplifying x = -1.128535534Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.557106964, -1.128535534}Solution
x = {4.557106964, -1.128535534}
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