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Simplifying 16x2 + -144x + -99 = 0 Reorder the terms: -99 + -144x + 16x2 = 0 Solving -99 + -144x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6.1875 + -9x + x2 = 0 Move the constant term to the right: Add '6.1875' to each side of the equation. -6.1875 + -9x + 6.1875 + x2 = 0 + 6.1875 Reorder the terms: -6.1875 + 6.1875 + -9x + x2 = 0 + 6.1875 Combine like terms: -6.1875 + 6.1875 = 0.0000 0.0000 + -9x + x2 = 0 + 6.1875 -9x + x2 = 0 + 6.1875 Combine like terms: 0 + 6.1875 = 6.1875 -9x + x2 = 6.1875 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 6.1875 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 6.1875 + 20.25 Combine like terms: 6.1875 + 20.25 = 26.4375 20.25 + -9x + x2 = 26.4375 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 26.4375 Calculate the square root of the right side: 5.14174095 Break this problem into two subproblems by setting (x + -4.5) equal to 5.14174095 and -5.14174095.Subproblem 1
x + -4.5 = 5.14174095 Simplifying x + -4.5 = 5.14174095 Reorder the terms: -4.5 + x = 5.14174095 Solving -4.5 + x = 5.14174095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 5.14174095 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.14174095 + 4.5 x = 5.14174095 + 4.5 Combine like terms: 5.14174095 + 4.5 = 9.64174095 x = 9.64174095 Simplifying x = 9.64174095Subproblem 2
x + -4.5 = -5.14174095 Simplifying x + -4.5 = -5.14174095 Reorder the terms: -4.5 + x = -5.14174095 Solving -4.5 + x = -5.14174095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -5.14174095 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.14174095 + 4.5 x = -5.14174095 + 4.5 Combine like terms: -5.14174095 + 4.5 = -0.64174095 x = -0.64174095 Simplifying x = -0.64174095Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.64174095, -0.64174095}
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