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Simplifying 3x2 + -24x + 37 = 0 Reorder the terms: 37 + -24x + 3x2 = 0 Solving 37 + -24x + 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'. 12.33333333 + -8x + x2 = 0 Move the constant term to the right: Add '-12.33333333' to each side of the equation. 12.33333333 + -8x + -12.33333333 + x2 = 0 + -12.33333333 Reorder the terms: 12.33333333 + -12.33333333 + -8x + x2 = 0 + -12.33333333 Combine like terms: 12.33333333 + -12.33333333 = 0.00000000 0.00000000 + -8x + x2 = 0 + -12.33333333 -8x + x2 = 0 + -12.33333333 Combine like terms: 0 + -12.33333333 = -12.33333333 -8x + x2 = -12.33333333 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -12.33333333 + 16 Reorder the terms: 16 + -8x + x2 = -12.33333333 + 16 Combine like terms: -12.33333333 + 16 = 3.66666667 16 + -8x + x2 = 3.66666667 Factor a perfect square on the left side: (x + -4)(x + -4) = 3.66666667 Calculate the square root of the right side: 1.914854216 Break this problem into two subproblems by setting (x + -4) equal to 1.914854216 and -1.914854216.Subproblem 1
x + -4 = 1.914854216 Simplifying x + -4 = 1.914854216 Reorder the terms: -4 + x = 1.914854216 Solving -4 + x = 1.914854216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 1.914854216 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.914854216 + 4 x = 1.914854216 + 4 Combine like terms: 1.914854216 + 4 = 5.914854216 x = 5.914854216 Simplifying x = 5.914854216Subproblem 2
x + -4 = -1.914854216 Simplifying x + -4 = -1.914854216 Reorder the terms: -4 + x = -1.914854216 Solving -4 + x = -1.914854216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -1.914854216 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.914854216 + 4 x = -1.914854216 + 4 Combine like terms: -1.914854216 + 4 = 2.085145784 x = 2.085145784 Simplifying x = 2.085145784Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.914854216, 2.085145784}
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