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Simplifying 3(x2 + -4x) = 77 Reorder the terms: 3(-4x + x2) = 77 (-4x * 3 + x2 * 3) = 77 (-12x + 3x2) = 77 Solving -12x + 3x2 = 77 Solving for variable 'x'. Reorder the terms: -77 + -12x + 3x2 = 77 + -77 Combine like terms: 77 + -77 = 0 -77 + -12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -25.66666667 + -4x + x2 = 0 Move the constant term to the right: Add '25.66666667' to each side of the equation. -25.66666667 + -4x + 25.66666667 + x2 = 0 + 25.66666667 Reorder the terms: -25.66666667 + 25.66666667 + -4x + x2 = 0 + 25.66666667 Combine like terms: -25.66666667 + 25.66666667 = 0.00000000 0.00000000 + -4x + x2 = 0 + 25.66666667 -4x + x2 = 0 + 25.66666667 Combine like terms: 0 + 25.66666667 = 25.66666667 -4x + x2 = 25.66666667 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 25.66666667 + 4 Reorder the terms: 4 + -4x + x2 = 25.66666667 + 4 Combine like terms: 25.66666667 + 4 = 29.66666667 4 + -4x + x2 = 29.66666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 29.66666667 Calculate the square root of the right side: 5.446711546 Break this problem into two subproblems by setting (x + -2) equal to 5.446711546 and -5.446711546.Subproblem 1
x + -2 = 5.446711546 Simplifying x + -2 = 5.446711546 Reorder the terms: -2 + x = 5.446711546 Solving -2 + x = 5.446711546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 5.446711546 + 2 Combine like terms: -2 + 2 = 0 0 + x = 5.446711546 + 2 x = 5.446711546 + 2 Combine like terms: 5.446711546 + 2 = 7.446711546 x = 7.446711546 Simplifying x = 7.446711546Subproblem 2
x + -2 = -5.446711546 Simplifying x + -2 = -5.446711546 Reorder the terms: -2 + x = -5.446711546 Solving -2 + x = -5.446711546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -5.446711546 + 2 Combine like terms: -2 + 2 = 0 0 + x = -5.446711546 + 2 x = -5.446711546 + 2 Combine like terms: -5.446711546 + 2 = -3.446711546 x = -3.446711546 Simplifying x = -3.446711546Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.446711546, -3.446711546}
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