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Simplifying 3x + -4(x2 + -6x + -7) = 6(x + -7) Reorder the terms: 3x + -4(-7 + -6x + x2) = 6(x + -7) 3x + (-7 * -4 + -6x * -4 + x2 * -4) = 6(x + -7) 3x + (28 + 24x + -4x2) = 6(x + -7) Reorder the terms: 28 + 3x + 24x + -4x2 = 6(x + -7) Combine like terms: 3x + 24x = 27x 28 + 27x + -4x2 = 6(x + -7) Reorder the terms: 28 + 27x + -4x2 = 6(-7 + x) 28 + 27x + -4x2 = (-7 * 6 + x * 6) 28 + 27x + -4x2 = (-42 + 6x) Solving 28 + 27x + -4x2 = -42 + 6x Solving for variable 'x'. Reorder the terms: 28 + 42 + 27x + -6x + -4x2 = -42 + 6x + 42 + -6x Combine like terms: 28 + 42 = 70 70 + 27x + -6x + -4x2 = -42 + 6x + 42 + -6x Combine like terms: 27x + -6x = 21x 70 + 21x + -4x2 = -42 + 6x + 42 + -6x Reorder the terms: 70 + 21x + -4x2 = -42 + 42 + 6x + -6x Combine like terms: -42 + 42 = 0 70 + 21x + -4x2 = 0 + 6x + -6x 70 + 21x + -4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 70 + 21x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -17.5 + -5.25x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -5.25x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -5.25x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -5.25x + x2 = 0 + 17.5 -5.25x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -5.25x + x2 = 17.5 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = 17.5 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = 17.5 + 6.890625 Combine like terms: 17.5 + 6.890625 = 24.390625 6.890625 + -5.25x + x2 = 24.390625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 24.390625 Calculate the square root of the right side: 4.938686566 Break this problem into two subproblems by setting (x + -2.625) equal to 4.938686566 and -4.938686566.Subproblem 1
x + -2.625 = 4.938686566 Simplifying x + -2.625 = 4.938686566 Reorder the terms: -2.625 + x = 4.938686566 Solving -2.625 + x = 4.938686566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 4.938686566 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 4.938686566 + 2.625 x = 4.938686566 + 2.625 Combine like terms: 4.938686566 + 2.625 = 7.563686566 x = 7.563686566 Simplifying x = 7.563686566Subproblem 2
x + -2.625 = -4.938686566 Simplifying x + -2.625 = -4.938686566 Reorder the terms: -2.625 + x = -4.938686566 Solving -2.625 + x = -4.938686566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -4.938686566 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -4.938686566 + 2.625 x = -4.938686566 + 2.625 Combine like terms: -4.938686566 + 2.625 = -2.313686566 x = -2.313686566 Simplifying x = -2.313686566Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.563686566, -2.313686566}
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