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Simplifying 0.75(x + -6)(x + -6) = 20 Reorder the terms: 0.75(-6 + x)(x + -6) = 20 Reorder the terms: 0.75(-6 + x)(-6 + x) = 20 Multiply (-6 + x) * (-6 + x) 0.75(-6(-6 + x) + x(-6 + x)) = 20 0.75((-6 * -6 + x * -6) + x(-6 + x)) = 20 0.75((36 + -6x) + x(-6 + x)) = 20 0.75(36 + -6x + (-6 * x + x * x)) = 20 0.75(36 + -6x + (-6x + x2)) = 20 Combine like terms: -6x + -6x = -12x 0.75(36 + -12x + x2) = 20 (36 * 0.75 + -12x * 0.75 + x2 * 0.75) = 20 (27 + -9x + 0.75x2) = 20 Solving 27 + -9x + 0.75x2 = 20 Solving for variable 'x'. Reorder the terms: 27 + -20 + -9x + 0.75x2 = 20 + -20 Combine like terms: 27 + -20 = 7 7 + -9x + 0.75x2 = 20 + -20 Combine like terms: 20 + -20 = 0 7 + -9x + 0.75x2 = 0 Begin completing the square. Divide all terms by 0.75 the coefficient of the squared term: Divide each side by '0.75'. 9.333333333 + -12x + x2 = 0 Move the constant term to the right: Add '-9.333333333' to each side of the equation. 9.333333333 + -12x + -9.333333333 + x2 = 0 + -9.333333333 Reorder the terms: 9.333333333 + -9.333333333 + -12x + x2 = 0 + -9.333333333 Combine like terms: 9.333333333 + -9.333333333 = 0.000000000 0.000000000 + -12x + x2 = 0 + -9.333333333 -12x + x2 = 0 + -9.333333333 Combine like terms: 0 + -9.333333333 = -9.333333333 -12x + x2 = -9.333333333 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -9.333333333 + 36 Reorder the terms: 36 + -12x + x2 = -9.333333333 + 36 Combine like terms: -9.333333333 + 36 = 26.666666667 36 + -12x + x2 = 26.666666667 Factor a perfect square on the left side: (x + -6)(x + -6) = 26.666666667 Calculate the square root of the right side: 5.163977795 Break this problem into two subproblems by setting (x + -6) equal to 5.163977795 and -5.163977795.Subproblem 1
x + -6 = 5.163977795 Simplifying x + -6 = 5.163977795 Reorder the terms: -6 + x = 5.163977795 Solving -6 + x = 5.163977795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.163977795 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.163977795 + 6 x = 5.163977795 + 6 Combine like terms: 5.163977795 + 6 = 11.163977795 x = 11.163977795 Simplifying x = 11.163977795Subproblem 2
x + -6 = -5.163977795 Simplifying x + -6 = -5.163977795 Reorder the terms: -6 + x = -5.163977795 Solving -6 + x = -5.163977795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.163977795 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.163977795 + 6 x = -5.163977795 + 6 Combine like terms: -5.163977795 + 6 = 0.836022205 x = 0.836022205 Simplifying x = 0.836022205Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.163977795, 0.836022205}
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