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Simplifying 4x2 + 96x = 51.3 Reorder the terms: 96x + 4x2 = 51.3 Solving 96x + 4x2 = 51.3 Solving for variable 'x'. Reorder the terms: -51.3 + 96x + 4x2 = 51.3 + -51.3 Combine like terms: 51.3 + -51.3 = 0.0 -51.3 + 96x + 4x2 = 0.0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.825 + 24x + x2 = 0.0 Move the constant term to the right: Add '12.825' to each side of the equation. -12.825 + 24x + 12.825 + x2 = 0.0 + 12.825 Reorder the terms: -12.825 + 12.825 + 24x + x2 = 0.0 + 12.825 Combine like terms: -12.825 + 12.825 = 0.000 0.000 + 24x + x2 = 0.0 + 12.825 24x + x2 = 0.0 + 12.825 Combine like terms: 0.0 + 12.825 = 12.825 24x + x2 = 12.825 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 12.825 + 144 Reorder the terms: 144 + 24x + x2 = 12.825 + 144 Combine like terms: 12.825 + 144 = 156.825 144 + 24x + x2 = 156.825 Factor a perfect square on the left side: (x + 12)(x + 12) = 156.825 Calculate the square root of the right side: 12.522978879 Break this problem into two subproblems by setting (x + 12) equal to 12.522978879 and -12.522978879.Subproblem 1
x + 12 = 12.522978879 Simplifying x + 12 = 12.522978879 Reorder the terms: 12 + x = 12.522978879 Solving 12 + x = 12.522978879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 12.522978879 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.522978879 + -12 x = 12.522978879 + -12 Combine like terms: 12.522978879 + -12 = 0.522978879 x = 0.522978879 Simplifying x = 0.522978879Subproblem 2
x + 12 = -12.522978879 Simplifying x + 12 = -12.522978879 Reorder the terms: 12 + x = -12.522978879 Solving 12 + x = -12.522978879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -12.522978879 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.522978879 + -12 x = -12.522978879 + -12 Combine like terms: -12.522978879 + -12 = -24.522978879 x = -24.522978879 Simplifying x = -24.522978879Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.522978879, -24.522978879}
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