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Simplifying (2x + -6)(2x + -6) = 21 Reorder the terms: (-6 + 2x)(2x + -6) = 21 Reorder the terms: (-6 + 2x)(-6 + 2x) = 21 Multiply (-6 + 2x) * (-6 + 2x) (-6(-6 + 2x) + 2x * (-6 + 2x)) = 21 ((-6 * -6 + 2x * -6) + 2x * (-6 + 2x)) = 21 ((36 + -12x) + 2x * (-6 + 2x)) = 21 (36 + -12x + (-6 * 2x + 2x * 2x)) = 21 (36 + -12x + (-12x + 4x2)) = 21 Combine like terms: -12x + -12x = -24x (36 + -24x + 4x2) = 21 Solving 36 + -24x + 4x2 = 21 Solving for variable 'x'. Reorder the terms: 36 + -21 + -24x + 4x2 = 21 + -21 Combine like terms: 36 + -21 = 15 15 + -24x + 4x2 = 21 + -21 Combine like terms: 21 + -21 = 0 15 + -24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -6x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -6x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -6x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -6x + x2 = 0 + -3.75 -6x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -6x + x2 = -3.75 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 = -3.75 + 9 Reorder the terms: 9 + -6x + x2 = -3.75 + 9 Combine like terms: -3.75 + 9 = 5.25 9 + -6x + x2 = 5.25 Factor a perfect square on the left side: (x + -3)(x + -3) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -3) equal to 2.291287847 and -2.291287847.Subproblem 1
x + -3 = 2.291287847 Simplifying x + -3 = 2.291287847 Reorder the terms: -3 + x = 2.291287847 Solving -3 + x = 2.291287847 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 = 2.291287847 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.291287847 + 3 x = 2.291287847 + 3 Combine like terms: 2.291287847 + 3 = 5.291287847 x = 5.291287847 Simplifying x = 5.291287847Subproblem 2
x + -3 = -2.291287847 Simplifying x + -3 = -2.291287847 Reorder the terms: -3 + x = -2.291287847 Solving -3 + x = -2.291287847 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 = -2.291287847 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.291287847 + 3 x = -2.291287847 + 3 Combine like terms: -2.291287847 + 3 = 0.708712153 x = 0.708712153 Simplifying x = 0.708712153Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.291287847, 0.708712153}
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