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Simplifying -3x(7x + -4) + 6x + -1(13 + -24x2) = 0 Reorder the terms: -3x(-4 + 7x) + 6x + -1(13 + -24x2) = 0 (-4 * -3x + 7x * -3x) + 6x + -1(13 + -24x2) = 0 (12x + -21x2) + 6x + -1(13 + -24x2) = 0 12x + -21x2 + 6x + (13 * -1 + -24x2 * -1) = 0 12x + -21x2 + 6x + (-13 + 24x2) = 0 Reorder the terms: -13 + 12x + 6x + -21x2 + 24x2 = 0 Combine like terms: 12x + 6x = 18x -13 + 18x + -21x2 + 24x2 = 0 Combine like terms: -21x2 + 24x2 = 3x2 -13 + 18x + 3x2 = 0 Solving -13 + 18x + 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'. -4.333333333 + 6x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + 6x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + 6x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + 6x + x2 = 0 + 4.333333333 6x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 6x + x2 = 4.333333333 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 4.333333333 + 9 Reorder the terms: 9 + 6x + x2 = 4.333333333 + 9 Combine like terms: 4.333333333 + 9 = 13.333333333 9 + 6x + x2 = 13.333333333 Factor a perfect square on the left side: (x + 3)(x + 3) = 13.333333333 Calculate the square root of the right side: 3.651483717 Break this problem into two subproblems by setting (x + 3) equal to 3.651483717 and -3.651483717.Subproblem 1
x + 3 = 3.651483717 Simplifying x + 3 = 3.651483717 Reorder the terms: 3 + x = 3.651483717 Solving 3 + x = 3.651483717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.651483717 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.651483717 + -3 x = 3.651483717 + -3 Combine like terms: 3.651483717 + -3 = 0.651483717 x = 0.651483717 Simplifying x = 0.651483717Subproblem 2
x + 3 = -3.651483717 Simplifying x + 3 = -3.651483717 Reorder the terms: 3 + x = -3.651483717 Solving 3 + x = -3.651483717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.651483717 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.651483717 + -3 x = -3.651483717 + -3 Combine like terms: -3.651483717 + -3 = -6.651483717 x = -6.651483717 Simplifying x = -6.651483717Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.651483717, -6.651483717}
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