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Simplifying (3x + -6)(3x + -6) = 21 Reorder the terms: (-6 + 3x)(3x + -6) = 21 Reorder the terms: (-6 + 3x)(-6 + 3x) = 21 Multiply (-6 + 3x) * (-6 + 3x) (-6(-6 + 3x) + 3x * (-6 + 3x)) = 21 ((-6 * -6 + 3x * -6) + 3x * (-6 + 3x)) = 21 ((36 + -18x) + 3x * (-6 + 3x)) = 21 (36 + -18x + (-6 * 3x + 3x * 3x)) = 21 (36 + -18x + (-18x + 9x2)) = 21 Combine like terms: -18x + -18x = -36x (36 + -36x + 9x2) = 21 Solving 36 + -36x + 9x2 = 21 Solving for variable 'x'. Reorder the terms: 36 + -21 + -36x + 9x2 = 21 + -21 Combine like terms: 36 + -21 = 15 15 + -36x + 9x2 = 21 + -21 Combine like terms: 21 + -21 = 0 15 + -36x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -12x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -12x + 3x2)' equal to zero and attempt to solve: Simplifying 5 + -12x + 3x2 = 0 Solving 5 + -12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -4x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -4x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -4x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -4x + x2 = 0 + -1.666666667 -4x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -4x + x2 = -1.666666667 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 = -1.666666667 + 4 Reorder the terms: 4 + -4x + x2 = -1.666666667 + 4 Combine like terms: -1.666666667 + 4 = 2.333333333 4 + -4x + x2 = 2.333333333 Factor a perfect square on the left side: (x + -2)(x + -2) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x + -2) equal to 1.527525232 and -1.527525232.Subproblem 1
x + -2 = 1.527525232 Simplifying x + -2 = 1.527525232 Reorder the terms: -2 + x = 1.527525232 Solving -2 + x = 1.527525232 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 = 1.527525232 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.527525232 + 2 x = 1.527525232 + 2 Combine like terms: 1.527525232 + 2 = 3.527525232 x = 3.527525232 Simplifying x = 3.527525232Subproblem 2
x + -2 = -1.527525232 Simplifying x + -2 = -1.527525232 Reorder the terms: -2 + x = -1.527525232 Solving -2 + x = -1.527525232 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 = -1.527525232 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.527525232 + 2 x = -1.527525232 + 2 Combine like terms: -1.527525232 + 2 = 0.472474768 x = 0.472474768 Simplifying x = 0.472474768Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.527525232, 0.472474768}Solution
x = {3.527525232, 0.472474768}
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