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Simplifying ((2x + -3)(2x + -3)) + -8x2 + 8x + 12 = 0 Reorder the terms: ((-3 + 2x)(2x + -3)) + -8x2 + 8x + 12 = 0 Reorder the terms: ((-3 + 2x)(-3 + 2x)) + -8x2 + 8x + 12 = 0 Multiply (-3 + 2x) * (-3 + 2x) ((-3(-3 + 2x) + 2x * (-3 + 2x))) + -8x2 + 8x + 12 = 0 (((-3 * -3 + 2x * -3) + 2x * (-3 + 2x))) + -8x2 + 8x + 12 = 0 (((9 + -6x) + 2x * (-3 + 2x))) + -8x2 + 8x + 12 = 0 ((9 + -6x + (-3 * 2x + 2x * 2x))) + -8x2 + 8x + 12 = 0 ((9 + -6x + (-6x + 4x2))) + -8x2 + 8x + 12 = 0 Combine like terms: -6x + -6x = -12x ((9 + -12x + 4x2)) + -8x2 + 8x + 12 = 0 (9 + -12x + 4x2) + -8x2 + 8x + 12 = 0 Remove parenthesis around (9 + -12x + 4x2) 9 + -12x + 4x2 + -8x2 + 8x + 12 = 0 Reorder the terms: 9 + 12 + -12x + 8x + 4x2 + -8x2 = 0 Combine like terms: 9 + 12 = 21 21 + -12x + 8x + 4x2 + -8x2 = 0 Combine like terms: -12x + 8x = -4x 21 + -4x + 4x2 + -8x2 = 0 Combine like terms: 4x2 + -8x2 = -4x2 21 + -4x + -4x2 = 0 Solving 21 + -4x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5.25 + x + x2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + x + 5.25 + x2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + x + x2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x + x2 = 0 + 5.25 x + x2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 x + x2 = 5.25 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 5.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 5.25 + 0.25 Combine like terms: 5.25 + 0.25 = 5.5 1.25 + x2 = 5.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (x + 0.5) equal to 2.34520788 and -2.34520788.Subproblem 1
x + 0.5 = 2.34520788 Simplifying x + 0.5 = 2.34520788 Reorder the terms: 0.5 + x = 2.34520788 Solving 0.5 + x = 2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.34520788 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.34520788 + -0.5 x = 2.34520788 + -0.5 Combine like terms: 2.34520788 + -0.5 = 1.84520788 x = 1.84520788 Simplifying x = 1.84520788Subproblem 2
x + 0.5 = -2.34520788 Simplifying x + 0.5 = -2.34520788 Reorder the terms: 0.5 + x = -2.34520788 Solving 0.5 + x = -2.34520788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.34520788 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.34520788 + -0.5 x = -2.34520788 + -0.5 Combine like terms: -2.34520788 + -0.5 = -2.84520788 x = -2.84520788 Simplifying x = -2.84520788Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.84520788, -2.84520788}
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