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Simplifying 10x(x + -8) = 3x + -66 Reorder the terms: 10x(-8 + x) = 3x + -66 (-8 * 10x + x * 10x) = 3x + -66 (-80x + 10x2) = 3x + -66 Reorder the terms: -80x + 10x2 = -66 + 3x Solving -80x + 10x2 = -66 + 3x Solving for variable 'x'. Reorder the terms: 66 + -80x + -3x + 10x2 = -66 + 3x + 66 + -3x Combine like terms: -80x + -3x = -83x 66 + -83x + 10x2 = -66 + 3x + 66 + -3x Reorder the terms: 66 + -83x + 10x2 = -66 + 66 + 3x + -3x Combine like terms: -66 + 66 = 0 66 + -83x + 10x2 = 0 + 3x + -3x 66 + -83x + 10x2 = 3x + -3x Combine like terms: 3x + -3x = 0 66 + -83x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 6.6 + -8.3x + x2 = 0 Move the constant term to the right: Add '-6.6' to each side of the equation. 6.6 + -8.3x + -6.6 + x2 = 0 + -6.6 Reorder the terms: 6.6 + -6.6 + -8.3x + x2 = 0 + -6.6 Combine like terms: 6.6 + -6.6 = 0.0 0.0 + -8.3x + x2 = 0 + -6.6 -8.3x + x2 = 0 + -6.6 Combine like terms: 0 + -6.6 = -6.6 -8.3x + x2 = -6.6 The x term is -8.3x. Take half its coefficient (-4.15). Square it (17.2225) and add it to both sides. Add '17.2225' to each side of the equation. -8.3x + 17.2225 + x2 = -6.6 + 17.2225 Reorder the terms: 17.2225 + -8.3x + x2 = -6.6 + 17.2225 Combine like terms: -6.6 + 17.2225 = 10.6225 17.2225 + -8.3x + x2 = 10.6225 Factor a perfect square on the left side: (x + -4.15)(x + -4.15) = 10.6225 Calculate the square root of the right side: 3.259217698 Break this problem into two subproblems by setting (x + -4.15) equal to 3.259217698 and -3.259217698.Subproblem 1
x + -4.15 = 3.259217698 Simplifying x + -4.15 = 3.259217698 Reorder the terms: -4.15 + x = 3.259217698 Solving -4.15 + x = 3.259217698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.15' to each side of the equation. -4.15 + 4.15 + x = 3.259217698 + 4.15 Combine like terms: -4.15 + 4.15 = 0.00 0.00 + x = 3.259217698 + 4.15 x = 3.259217698 + 4.15 Combine like terms: 3.259217698 + 4.15 = 7.409217698 x = 7.409217698 Simplifying x = 7.409217698Subproblem 2
x + -4.15 = -3.259217698 Simplifying x + -4.15 = -3.259217698 Reorder the terms: -4.15 + x = -3.259217698 Solving -4.15 + x = -3.259217698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.15' to each side of the equation. -4.15 + 4.15 + x = -3.259217698 + 4.15 Combine like terms: -4.15 + 4.15 = 0.00 0.00 + x = -3.259217698 + 4.15 x = -3.259217698 + 4.15 Combine like terms: -3.259217698 + 4.15 = 0.890782302 x = 0.890782302 Simplifying x = 0.890782302Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.409217698, 0.890782302}
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