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Simplifying 16x2 + -12x + 9 = 144 Reorder the terms: 9 + -12x + 16x2 = 144 Solving 9 + -12x + 16x2 = 144 Solving for variable 'x'. Reorder the terms: 9 + -144 + -12x + 16x2 = 144 + -144 Combine like terms: 9 + -144 = -135 -135 + -12x + 16x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -135 + -12x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -8.4375 + -0.75x + x2 = 0 Move the constant term to the right: Add '8.4375' to each side of the equation. -8.4375 + -0.75x + 8.4375 + x2 = 0 + 8.4375 Reorder the terms: -8.4375 + 8.4375 + -0.75x + x2 = 0 + 8.4375 Combine like terms: -8.4375 + 8.4375 = 0.0000 0.0000 + -0.75x + x2 = 0 + 8.4375 -0.75x + x2 = 0 + 8.4375 Combine like terms: 0 + 8.4375 = 8.4375 -0.75x + x2 = 8.4375 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 8.4375 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 8.4375 + 0.140625 Combine like terms: 8.4375 + 0.140625 = 8.578125 0.140625 + -0.75x + x2 = 8.578125 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 8.578125 Calculate the square root of the right side: 2.928843628 Break this problem into two subproblems by setting (x + -0.375) equal to 2.928843628 and -2.928843628.Subproblem 1
x + -0.375 = 2.928843628 Simplifying x + -0.375 = 2.928843628 Reorder the terms: -0.375 + x = 2.928843628 Solving -0.375 + x = 2.928843628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 2.928843628 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 2.928843628 + 0.375 x = 2.928843628 + 0.375 Combine like terms: 2.928843628 + 0.375 = 3.303843628 x = 3.303843628 Simplifying x = 3.303843628Subproblem 2
x + -0.375 = -2.928843628 Simplifying x + -0.375 = -2.928843628 Reorder the terms: -0.375 + x = -2.928843628 Solving -0.375 + x = -2.928843628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -2.928843628 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -2.928843628 + 0.375 x = -2.928843628 + 0.375 Combine like terms: -2.928843628 + 0.375 = -2.553843628 x = -2.553843628 Simplifying x = -2.553843628Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.303843628, -2.553843628}
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