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Simplifying 8.88 = 14x + (1 + -1x)(6) * x Reorder the terms for easier multiplication: 8.88 = 14x + 6x(1 + -1x) 8.88 = 14x + (1 * 6x + -1x * 6x) 8.88 = 14x + (6x + -6x2) Combine like terms: 14x + 6x = 20x 8.88 = 20x + -6x2 Solving 8.88 = 20x + -6x2 Solving for variable 'x'. Reorder the terms: 8.88 + -20x + 6x2 = 20x + -20x + -6x2 + 6x2 Combine like terms: 20x + -20x = 0 8.88 + -20x + 6x2 = 0 + -6x2 + 6x2 8.88 + -20x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 8.88 + -20x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.48 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-1.48' to each side of the equation. 1.48 + -3.333333333x + -1.48 + x2 = 0 + -1.48 Reorder the terms: 1.48 + -1.48 + -3.333333333x + x2 = 0 + -1.48 Combine like terms: 1.48 + -1.48 = 0.00 0.00 + -3.333333333x + x2 = 0 + -1.48 -3.333333333x + x2 = 0 + -1.48 Combine like terms: 0 + -1.48 = -1.48 -3.333333333x + x2 = -1.48 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = -1.48 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -1.48 + 2.777777779 Combine like terms: -1.48 + 2.777777779 = 1.297777779 2.777777779 + -3.333333333x + x2 = 1.297777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 1.297777779 Calculate the square root of the right side: 1.1392005 Break this problem into two subproblems by setting (x + -1.666666667) equal to 1.1392005 and -1.1392005.Subproblem 1
x + -1.666666667 = 1.1392005 Simplifying x + -1.666666667 = 1.1392005 Reorder the terms: -1.666666667 + x = 1.1392005 Solving -1.666666667 + x = 1.1392005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 1.1392005 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 1.1392005 + 1.666666667 x = 1.1392005 + 1.666666667 Combine like terms: 1.1392005 + 1.666666667 = 2.805867167 x = 2.805867167 Simplifying x = 2.805867167Subproblem 2
x + -1.666666667 = -1.1392005 Simplifying x + -1.666666667 = -1.1392005 Reorder the terms: -1.666666667 + x = -1.1392005 Solving -1.666666667 + x = -1.1392005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -1.1392005 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -1.1392005 + 1.666666667 x = -1.1392005 + 1.666666667 Combine like terms: -1.1392005 + 1.666666667 = 0.527466167 x = 0.527466167 Simplifying x = 0.527466167Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.805867167, 0.527466167}
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