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Simplifying 16x2 + 150x + 5 = 12 Reorder the terms: 5 + 150x + 16x2 = 12 Solving 5 + 150x + 16x2 = 12 Solving for variable 'x'. Reorder the terms: 5 + -12 + 150x + 16x2 = 12 + -12 Combine like terms: 5 + -12 = -7 -7 + 150x + 16x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -7 + 150x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + 9.375x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + 9.375x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + 9.375x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + 9.375x + x2 = 0 + 0.4375 9.375x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 9.375x + x2 = 0.4375 The x term is 9.375x. Take half its coefficient (4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. 9.375x + 21.97265625 + x2 = 0.4375 + 21.97265625 Reorder the terms: 21.97265625 + 9.375x + x2 = 0.4375 + 21.97265625 Combine like terms: 0.4375 + 21.97265625 = 22.41015625 21.97265625 + 9.375x + x2 = 22.41015625 Factor a perfect square on the left side: (x + 4.6875)(x + 4.6875) = 22.41015625 Calculate the square root of the right side: 4.733936655 Break this problem into two subproblems by setting (x + 4.6875) equal to 4.733936655 and -4.733936655.Subproblem 1
x + 4.6875 = 4.733936655 Simplifying x + 4.6875 = 4.733936655 Reorder the terms: 4.6875 + x = 4.733936655 Solving 4.6875 + x = 4.733936655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + x = 4.733936655 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + x = 4.733936655 + -4.6875 x = 4.733936655 + -4.6875 Combine like terms: 4.733936655 + -4.6875 = 0.046436655 x = 0.046436655 Simplifying x = 0.046436655Subproblem 2
x + 4.6875 = -4.733936655 Simplifying x + 4.6875 = -4.733936655 Reorder the terms: 4.6875 + x = -4.733936655 Solving 4.6875 + x = -4.733936655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + x = -4.733936655 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + x = -4.733936655 + -4.6875 x = -4.733936655 + -4.6875 Combine like terms: -4.733936655 + -4.6875 = -9.421436655 x = -9.421436655 Simplifying x = -9.421436655Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.046436655, -9.421436655}
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