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Simplifying 3((x2) + -2x + -10) = 14 3(x2 + -2x + -10) = 14 Reorder the terms: 3(-10 + -2x + x2) = 14 (-10 * 3 + -2x * 3 + x2 * 3) = 14 (-30 + -6x + 3x2) = 14 Solving -30 + -6x + 3x2 = 14 Solving for variable 'x'. Reorder the terms: -30 + -14 + -6x + 3x2 = 14 + -14 Combine like terms: -30 + -14 = -44 -44 + -6x + 3x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -44 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -14.66666667 + -2x + x2 = 0 Move the constant term to the right: Add '14.66666667' to each side of the equation. -14.66666667 + -2x + 14.66666667 + x2 = 0 + 14.66666667 Reorder the terms: -14.66666667 + 14.66666667 + -2x + x2 = 0 + 14.66666667 Combine like terms: -14.66666667 + 14.66666667 = 0.00000000 0.00000000 + -2x + x2 = 0 + 14.66666667 -2x + x2 = 0 + 14.66666667 Combine like terms: 0 + 14.66666667 = 14.66666667 -2x + x2 = 14.66666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 14.66666667 + 1 Reorder the terms: 1 + -2x + x2 = 14.66666667 + 1 Combine like terms: 14.66666667 + 1 = 15.66666667 1 + -2x + x2 = 15.66666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 15.66666667 Calculate the square root of the right side: 3.958114029 Break this problem into two subproblems by setting (x + -1) equal to 3.958114029 and -3.958114029.Subproblem 1
x + -1 = 3.958114029 Simplifying x + -1 = 3.958114029 Reorder the terms: -1 + x = 3.958114029 Solving -1 + x = 3.958114029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.958114029 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.958114029 + 1 x = 3.958114029 + 1 Combine like terms: 3.958114029 + 1 = 4.958114029 x = 4.958114029 Simplifying x = 4.958114029Subproblem 2
x + -1 = -3.958114029 Simplifying x + -1 = -3.958114029 Reorder the terms: -1 + x = -3.958114029 Solving -1 + x = -3.958114029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.958114029 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.958114029 + 1 x = -3.958114029 + 1 Combine like terms: -3.958114029 + 1 = -2.958114029 x = -2.958114029 Simplifying x = -2.958114029Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.958114029, -2.958114029}
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