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Simplifying 2(3 + -6x) = 2x(24 + -1x) (3 * 2 + -6x * 2) = 2x(24 + -1x) (6 + -12x) = 2x(24 + -1x) 6 + -12x = (24 * 2x + -1x * 2x) 6 + -12x = (48x + -2x2) Solving 6 + -12x = 48x + -2x2 Solving for variable 'x'. Combine like terms: -12x + -48x = -60x 6 + -60x + 2x2 = 48x + -2x2 + -48x + 2x2 Reorder the terms: 6 + -60x + 2x2 = 48x + -48x + -2x2 + 2x2 Combine like terms: 48x + -48x = 0 6 + -60x + 2x2 = 0 + -2x2 + 2x2 6 + -60x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 6 + -60x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -30x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -30x + x2)' equal to zero and attempt to solve: Simplifying 3 + -30x + x2 = 0 Solving 3 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -30x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -30x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -30x + x2 = 0 + -3 -30x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -30x + x2 = -3 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -3 + 225 Reorder the terms: 225 + -30x + x2 = -3 + 225 Combine like terms: -3 + 225 = 222 225 + -30x + x2 = 222 Factor a perfect square on the left side: (x + -15)(x + -15) = 222 Calculate the square root of the right side: 14.899664426 Break this problem into two subproblems by setting (x + -15) equal to 14.899664426 and -14.899664426.Subproblem 1
x + -15 = 14.899664426 Simplifying x + -15 = 14.899664426 Reorder the terms: -15 + x = 14.899664426 Solving -15 + x = 14.899664426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 14.899664426 + 15 Combine like terms: -15 + 15 = 0 0 + x = 14.899664426 + 15 x = 14.899664426 + 15 Combine like terms: 14.899664426 + 15 = 29.899664426 x = 29.899664426 Simplifying x = 29.899664426Subproblem 2
x + -15 = -14.899664426 Simplifying x + -15 = -14.899664426 Reorder the terms: -15 + x = -14.899664426 Solving -15 + x = -14.899664426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -14.899664426 + 15 Combine like terms: -15 + 15 = 0 0 + x = -14.899664426 + 15 x = -14.899664426 + 15 Combine like terms: -14.899664426 + 15 = 0.100335574 x = 0.100335574 Simplifying x = 0.100335574Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.899664426, 0.100335574}Solution
x = {29.899664426, 0.100335574}
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