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Simplifying 5(X + -3)(X + -3) = 30 Reorder the terms: 5(-3 + X)(X + -3) = 30 Reorder the terms: 5(-3 + X)(-3 + X) = 30 Multiply (-3 + X) * (-3 + X) 5(-3(-3 + X) + X(-3 + X)) = 30 5((-3 * -3 + X * -3) + X(-3 + X)) = 30 5((9 + -3X) + X(-3 + X)) = 30 5(9 + -3X + (-3 * X + X * X)) = 30 5(9 + -3X + (-3X + X2)) = 30 Combine like terms: -3X + -3X = -6X 5(9 + -6X + X2) = 30 (9 * 5 + -6X * 5 + X2 * 5) = 30 (45 + -30X + 5X2) = 30 Solving 45 + -30X + 5X2 = 30 Solving for variable 'X'. Reorder the terms: 45 + -30 + -30X + 5X2 = 30 + -30 Combine like terms: 45 + -30 = 15 15 + -30X + 5X2 = 30 + -30 Combine like terms: 30 + -30 = 0 15 + -30X + 5X2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -6X + X2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -6X + X2)' equal to zero and attempt to solve: Simplifying 3 + -6X + X2 = 0 Solving 3 + -6X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6X + -3 + X2 = 0 + -3 Reorder the terms: 3 + -3 + -6X + X2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6X + X2 = 0 + -3 -6X + X2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6X + X2 = -3 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 = -3 + 9 Reorder the terms: 9 + -6X + X2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + -6X + X2 = 6 Factor a perfect square on the left side: (X + -3)(X + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (X + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
X + -3 = 2.449489743 Simplifying X + -3 = 2.449489743 Reorder the terms: -3 + X = 2.449489743 Solving -3 + X = 2.449489743 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 = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + X = 2.449489743 + 3 X = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 X = 5.449489743 Simplifying X = 5.449489743Subproblem 2
X + -3 = -2.449489743 Simplifying X + -3 = -2.449489743 Reorder the terms: -3 + X = -2.449489743 Solving -3 + X = -2.449489743 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 = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + X = -2.449489743 + 3 X = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 X = 0.550510257 Simplifying X = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.449489743, 0.550510257}Solution
X = {5.449489743, 0.550510257}
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