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Simplifying 5 = -3(x + 2)(x + -3) Reorder the terms: 5 = -3(2 + x)(x + -3) Reorder the terms: 5 = -3(2 + x)(-3 + x) Multiply (2 + x) * (-3 + x) 5 = -3(2(-3 + x) + x(-3 + x)) 5 = -3((-3 * 2 + x * 2) + x(-3 + x)) 5 = -3((-6 + 2x) + x(-3 + x)) 5 = -3(-6 + 2x + (-3 * x + x * x)) 5 = -3(-6 + 2x + (-3x + x2)) Combine like terms: 2x + -3x = -1x 5 = -3(-6 + -1x + x2) 5 = (-6 * -3 + -1x * -3 + x2 * -3) 5 = (18 + 3x + -3x2) Solving 5 = 18 + 3x + -3x2 Solving for variable 'x'. Combine like terms: 5 + -18 = -13 -13 + -3x + 3x2 = 18 + 3x + -3x2 + -18 + -3x + 3x2 Reorder the terms: -13 + -3x + 3x2 = 18 + -18 + 3x + -3x + -3x2 + 3x2 Combine like terms: 18 + -18 = 0 -13 + -3x + 3x2 = 0 + 3x + -3x + -3x2 + 3x2 -13 + -3x + 3x2 = 3x + -3x + -3x2 + 3x2 Combine like terms: 3x + -3x = 0 -13 + -3x + 3x2 = 0 + -3x2 + 3x2 -13 + -3x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -13 + -3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.333333333 + -1x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + -1x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + -1x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + -1x + x2 = 0 + 4.333333333 -1x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 -1x + x2 = 4.333333333 The x term is -1x. 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. -1x + 0.25 + x2 = 4.333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 4.333333333 + 0.25 Combine like terms: 4.333333333 + 0.25 = 4.583333333 0.25 + -1x + x2 = 4.583333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 4.583333333 Calculate the square root of the right side: 2.140872096 Break this problem into two subproblems by setting (x + -0.5) equal to 2.140872096 and -2.140872096.Subproblem 1
x + -0.5 = 2.140872096 Simplifying x + -0.5 = 2.140872096 Reorder the terms: -0.5 + x = 2.140872096 Solving -0.5 + x = 2.140872096 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 = 2.140872096 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.140872096 + 0.5 x = 2.140872096 + 0.5 Combine like terms: 2.140872096 + 0.5 = 2.640872096 x = 2.640872096 Simplifying x = 2.640872096Subproblem 2
x + -0.5 = -2.140872096 Simplifying x + -0.5 = -2.140872096 Reorder the terms: -0.5 + x = -2.140872096 Solving -0.5 + x = -2.140872096 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 = -2.140872096 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.140872096 + 0.5 x = -2.140872096 + 0.5 Combine like terms: -2.140872096 + 0.5 = -1.640872096 x = -1.640872096 Simplifying x = -1.640872096Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.640872096, -1.640872096}
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