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Simplifying -6x2 + 3x2 + 72x + -5 = 0 Reorder the terms: -5 + 72x + -6x2 + 3x2 = 0 Combine like terms: -6x2 + 3x2 = -3x2 -5 + 72x + -3x2 = 0 Solving -5 + 72x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.666666667 + -24x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -24x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -24x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -24x + x2 = 0 + -1.666666667 -24x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -24x + x2 = -1.666666667 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 = -1.666666667 + 144 Reorder the terms: 144 + -24x + x2 = -1.666666667 + 144 Combine like terms: -1.666666667 + 144 = 142.333333333 144 + -24x + x2 = 142.333333333 Factor a perfect square on the left side: (x + -12)(x + -12) = 142.333333333 Calculate the square root of the right side: 11.930353445 Break this problem into two subproblems by setting (x + -12) equal to 11.930353445 and -11.930353445.Subproblem 1
x + -12 = 11.930353445 Simplifying x + -12 = 11.930353445 Reorder the terms: -12 + x = 11.930353445 Solving -12 + x = 11.930353445 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 = 11.930353445 + 12 Combine like terms: -12 + 12 = 0 0 + x = 11.930353445 + 12 x = 11.930353445 + 12 Combine like terms: 11.930353445 + 12 = 23.930353445 x = 23.930353445 Simplifying x = 23.930353445Subproblem 2
x + -12 = -11.930353445 Simplifying x + -12 = -11.930353445 Reorder the terms: -12 + x = -11.930353445 Solving -12 + x = -11.930353445 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 = -11.930353445 + 12 Combine like terms: -12 + 12 = 0 0 + x = -11.930353445 + 12 x = -11.930353445 + 12 Combine like terms: -11.930353445 + 12 = 0.069646555 x = 0.069646555 Simplifying x = 0.069646555Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.930353445, 0.069646555}
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