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Simplifying -3x(2x + -3) = 4(3x + -2) + 1 Reorder the terms: -3x(-3 + 2x) = 4(3x + -2) + 1 (-3 * -3x + 2x * -3x) = 4(3x + -2) + 1 (9x + -6x2) = 4(3x + -2) + 1 Reorder the terms: 9x + -6x2 = 4(-2 + 3x) + 1 9x + -6x2 = (-2 * 4 + 3x * 4) + 1 9x + -6x2 = (-8 + 12x) + 1 Reorder the terms: 9x + -6x2 = -8 + 1 + 12x Combine like terms: -8 + 1 = -7 9x + -6x2 = -7 + 12x Solving 9x + -6x2 = -7 + 12x Solving for variable 'x'. Reorder the terms: 7 + 9x + -12x + -6x2 = -7 + 12x + 7 + -12x Combine like terms: 9x + -12x = -3x 7 + -3x + -6x2 = -7 + 12x + 7 + -12x Reorder the terms: 7 + -3x + -6x2 = -7 + 7 + 12x + -12x Combine like terms: -7 + 7 = 0 7 + -3x + -6x2 = 0 + 12x + -12x 7 + -3x + -6x2 = 12x + -12x Combine like terms: 12x + -12x = 0 7 + -3x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.166666667 + 0.5x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + 0.5x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + 0.5x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + 1.166666667 0.5x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 0.5x + x2 = 1.166666667 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1.166666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.166666667 + 0.0625 Combine like terms: 1.166666667 + 0.0625 = 1.229166667 0.0625 + 0.5x + x2 = 1.229166667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.229166667 Calculate the square root of the right side: 1.108677891 Break this problem into two subproblems by setting (x + 0.25) equal to 1.108677891 and -1.108677891.Subproblem 1
x + 0.25 = 1.108677891 Simplifying x + 0.25 = 1.108677891 Reorder the terms: 0.25 + x = 1.108677891 Solving 0.25 + x = 1.108677891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.108677891 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.108677891 + -0.25 x = 1.108677891 + -0.25 Combine like terms: 1.108677891 + -0.25 = 0.858677891 x = 0.858677891 Simplifying x = 0.858677891Subproblem 2
x + 0.25 = -1.108677891 Simplifying x + 0.25 = -1.108677891 Reorder the terms: 0.25 + x = -1.108677891 Solving 0.25 + x = -1.108677891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.108677891 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.108677891 + -0.25 x = -1.108677891 + -0.25 Combine like terms: -1.108677891 + -0.25 = -1.358677891 x = -1.358677891 Simplifying x = -1.358677891Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.858677891, -1.358677891}
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