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Simplifying -3x2 + 24x = 25 Reorder the terms: 24x + -3x2 = 25 Solving 24x + -3x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 24x + -3x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 24x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 8.333333333 + -8x + x2 = 0 Move the constant term to the right: Add '-8.333333333' to each side of the equation. 8.333333333 + -8x + -8.333333333 + x2 = 0 + -8.333333333 Reorder the terms: 8.333333333 + -8.333333333 + -8x + x2 = 0 + -8.333333333 Combine like terms: 8.333333333 + -8.333333333 = 0.000000000 0.000000000 + -8x + x2 = 0 + -8.333333333 -8x + x2 = 0 + -8.333333333 Combine like terms: 0 + -8.333333333 = -8.333333333 -8x + x2 = -8.333333333 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 = -8.333333333 + 16 Reorder the terms: 16 + -8x + x2 = -8.333333333 + 16 Combine like terms: -8.333333333 + 16 = 7.666666667 16 + -8x + x2 = 7.666666667 Factor a perfect square on the left side: (x + -4)(x + -4) = 7.666666667 Calculate the square root of the right side: 2.768874621 Break this problem into two subproblems by setting (x + -4) equal to 2.768874621 and -2.768874621.Subproblem 1
x + -4 = 2.768874621 Simplifying x + -4 = 2.768874621 Reorder the terms: -4 + x = 2.768874621 Solving -4 + x = 2.768874621 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 = 2.768874621 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.768874621 + 4 x = 2.768874621 + 4 Combine like terms: 2.768874621 + 4 = 6.768874621 x = 6.768874621 Simplifying x = 6.768874621Subproblem 2
x + -4 = -2.768874621 Simplifying x + -4 = -2.768874621 Reorder the terms: -4 + x = -2.768874621 Solving -4 + x = -2.768874621 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 = -2.768874621 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.768874621 + 4 x = -2.768874621 + 4 Combine like terms: -2.768874621 + 4 = 1.231125379 x = 1.231125379 Simplifying x = 1.231125379Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.768874621, 1.231125379}
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