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Simplifying (2x + -6)(2x + -6) = 19 Reorder the terms: (-6 + 2x)(2x + -6) = 19 Reorder the terms: (-6 + 2x)(-6 + 2x) = 19 Multiply (-6 + 2x) * (-6 + 2x) (-6(-6 + 2x) + 2x * (-6 + 2x)) = 19 ((-6 * -6 + 2x * -6) + 2x * (-6 + 2x)) = 19 ((36 + -12x) + 2x * (-6 + 2x)) = 19 (36 + -12x + (-6 * 2x + 2x * 2x)) = 19 (36 + -12x + (-12x + 4x2)) = 19 Combine like terms: -12x + -12x = -24x (36 + -24x + 4x2) = 19 Solving 36 + -24x + 4x2 = 19 Solving for variable 'x'. Reorder the terms: 36 + -19 + -24x + 4x2 = 19 + -19 Combine like terms: 36 + -19 = 17 17 + -24x + 4x2 = 19 + -19 Combine like terms: 19 + -19 = 0 17 + -24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.25 + -6x + x2 = 0 Move the constant term to the right: Add '-4.25' to each side of the equation. 4.25 + -6x + -4.25 + x2 = 0 + -4.25 Reorder the terms: 4.25 + -4.25 + -6x + x2 = 0 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + -6x + x2 = 0 + -4.25 -6x + x2 = 0 + -4.25 Combine like terms: 0 + -4.25 = -4.25 -6x + x2 = -4.25 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 = -4.25 + 9 Reorder the terms: 9 + -6x + x2 = -4.25 + 9 Combine like terms: -4.25 + 9 = 4.75 9 + -6x + x2 = 4.75 Factor a perfect square on the left side: (x + -3)(x + -3) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + -3) equal to 2.179449472 and -2.179449472.Subproblem 1
x + -3 = 2.179449472 Simplifying x + -3 = 2.179449472 Reorder the terms: -3 + x = 2.179449472 Solving -3 + x = 2.179449472 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 = 2.179449472 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.179449472 + 3 x = 2.179449472 + 3 Combine like terms: 2.179449472 + 3 = 5.179449472 x = 5.179449472 Simplifying x = 5.179449472Subproblem 2
x + -3 = -2.179449472 Simplifying x + -3 = -2.179449472 Reorder the terms: -3 + x = -2.179449472 Solving -3 + x = -2.179449472 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 = -2.179449472 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.179449472 + 3 x = -2.179449472 + 3 Combine like terms: -2.179449472 + 3 = 0.820550528 x = 0.820550528 Simplifying x = 0.820550528Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.179449472, 0.820550528}
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