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Simplifying 0 = 12x2 + -1x + -224 Reorder the terms: 0 = -224 + -1x + 12x2 Solving 0 = -224 + -1x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 224 = 224 224 + x + -12x2 = -224 + -1x + 12x2 + 224 + x + -12x2 Reorder the terms: 224 + x + -12x2 = -224 + 224 + -1x + x + 12x2 + -12x2 Combine like terms: -224 + 224 = 0 224 + x + -12x2 = 0 + -1x + x + 12x2 + -12x2 224 + x + -12x2 = -1x + x + 12x2 + -12x2 Combine like terms: -1x + x = 0 224 + x + -12x2 = 0 + 12x2 + -12x2 224 + x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 224 + x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -18.66666667 + -0.08333333333x + x2 = 0 Move the constant term to the right: Add '18.66666667' to each side of the equation. -18.66666667 + -0.08333333333x + 18.66666667 + x2 = 0 + 18.66666667 Reorder the terms: -18.66666667 + 18.66666667 + -0.08333333333x + x2 = 0 + 18.66666667 Combine like terms: -18.66666667 + 18.66666667 = 0.00000000 0.00000000 + -0.08333333333x + x2 = 0 + 18.66666667 -0.08333333333x + x2 = 0 + 18.66666667 Combine like terms: 0 + 18.66666667 = 18.66666667 -0.08333333333x + x2 = 18.66666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.08333333333x + 0.25 + x2 = 18.66666667 + 0.25 Reorder the terms: 0.25 + -0.08333333333x + x2 = 18.66666667 + 0.25 Combine like terms: 18.66666667 + 0.25 = 18.91666667 0.25 + -0.08333333333x + x2 = 18.91666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 18.91666667 Calculate the square root of the right side: 4.349329451 Break this problem into two subproblems by setting (x + 0.5) equal to 4.349329451 and -4.349329451.Subproblem 1
x + 0.5 = 4.349329451 Simplifying x + 0.5 = 4.349329451 Reorder the terms: 0.5 + x = 4.349329451 Solving 0.5 + x = 4.349329451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.349329451 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.349329451 + -0.5 x = 4.349329451 + -0.5 Combine like terms: 4.349329451 + -0.5 = 3.849329451 x = 3.849329451 Simplifying x = 3.849329451Subproblem 2
x + 0.5 = -4.349329451 Simplifying x + 0.5 = -4.349329451 Reorder the terms: 0.5 + x = -4.349329451 Solving 0.5 + x = -4.349329451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.349329451 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.349329451 + -0.5 x = -4.349329451 + -0.5 Combine like terms: -4.349329451 + -0.5 = -4.849329451 x = -4.849329451 Simplifying x = -4.849329451Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.849329451, -4.849329451}
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