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Simplifying 3(x + -2)(x + -2) = 450 Reorder the terms: 3(-2 + x)(x + -2) = 450 Reorder the terms: 3(-2 + x)(-2 + x) = 450 Multiply (-2 + x) * (-2 + x) 3(-2(-2 + x) + x(-2 + x)) = 450 3((-2 * -2 + x * -2) + x(-2 + x)) = 450 3((4 + -2x) + x(-2 + x)) = 450 3(4 + -2x + (-2 * x + x * x)) = 450 3(4 + -2x + (-2x + x2)) = 450 Combine like terms: -2x + -2x = -4x 3(4 + -4x + x2) = 450 (4 * 3 + -4x * 3 + x2 * 3) = 450 (12 + -12x + 3x2) = 450 Solving 12 + -12x + 3x2 = 450 Solving for variable 'x'. Reorder the terms: 12 + -450 + -12x + 3x2 = 450 + -450 Combine like terms: 12 + -450 = -438 -438 + -12x + 3x2 = 450 + -450 Combine like terms: 450 + -450 = 0 -438 + -12x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-146 + -4x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-146 + -4x + x2)' equal to zero and attempt to solve: Simplifying -146 + -4x + x2 = 0 Solving -146 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '146' to each side of the equation. -146 + -4x + 146 + x2 = 0 + 146 Reorder the terms: -146 + 146 + -4x + x2 = 0 + 146 Combine like terms: -146 + 146 = 0 0 + -4x + x2 = 0 + 146 -4x + x2 = 0 + 146 Combine like terms: 0 + 146 = 146 -4x + x2 = 146 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 146 + 4 Reorder the terms: 4 + -4x + x2 = 146 + 4 Combine like terms: 146 + 4 = 150 4 + -4x + x2 = 150 Factor a perfect square on the left side: (x + -2)(x + -2) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (x + -2) equal to 12.247448714 and -12.247448714.Subproblem 1
x + -2 = 12.247448714 Simplifying x + -2 = 12.247448714 Reorder the terms: -2 + x = 12.247448714 Solving -2 + x = 12.247448714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 12.247448714 + 2 Combine like terms: -2 + 2 = 0 0 + x = 12.247448714 + 2 x = 12.247448714 + 2 Combine like terms: 12.247448714 + 2 = 14.247448714 x = 14.247448714 Simplifying x = 14.247448714Subproblem 2
x + -2 = -12.247448714 Simplifying x + -2 = -12.247448714 Reorder the terms: -2 + x = -12.247448714 Solving -2 + x = -12.247448714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -12.247448714 + 2 Combine like terms: -2 + 2 = 0 0 + x = -12.247448714 + 2 x = -12.247448714 + 2 Combine like terms: -12.247448714 + 2 = -10.247448714 x = -10.247448714 Simplifying x = -10.247448714Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.247448714, -10.247448714}Solution
x = {14.247448714, -10.247448714}
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