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Simplifying -8(14x + 2) = 19(5 + -5x) + -35x(14x + -21) * 3 Reorder the terms: -8(2 + 14x) = 19(5 + -5x) + -35x(14x + -21) * 3 (2 * -8 + 14x * -8) = 19(5 + -5x) + -35x(14x + -21) * 3 (-16 + -112x) = 19(5 + -5x) + -35x(14x + -21) * 3 -16 + -112x = (5 * 19 + -5x * 19) + -35x(14x + -21) * 3 -16 + -112x = (95 + -95x) + -35x(14x + -21) * 3 Reorder the terms: -16 + -112x = 95 + -95x + -35x(-21 + 14x) * 3 Reorder the terms for easier multiplication: -16 + -112x = 95 + -95x + -35 * 3x(-21 + 14x) Multiply -35 * 3 -16 + -112x = 95 + -95x + -105x(-21 + 14x) -16 + -112x = 95 + -95x + (-21 * -105x + 14x * -105x) -16 + -112x = 95 + -95x + (2205x + -1470x2) Combine like terms: -95x + 2205x = 2110x -16 + -112x = 95 + 2110x + -1470x2 Solving -16 + -112x = 95 + 2110x + -1470x2 Solving for variable 'x'. Reorder the terms: -16 + -95 + -112x + -2110x + 1470x2 = 95 + 2110x + -1470x2 + -95 + -2110x + 1470x2 Combine like terms: -16 + -95 = -111 -111 + -112x + -2110x + 1470x2 = 95 + 2110x + -1470x2 + -95 + -2110x + 1470x2 Combine like terms: -112x + -2110x = -2222x -111 + -2222x + 1470x2 = 95 + 2110x + -1470x2 + -95 + -2110x + 1470x2 Reorder the terms: -111 + -2222x + 1470x2 = 95 + -95 + 2110x + -2110x + -1470x2 + 1470x2 Combine like terms: 95 + -95 = 0 -111 + -2222x + 1470x2 = 0 + 2110x + -2110x + -1470x2 + 1470x2 -111 + -2222x + 1470x2 = 2110x + -2110x + -1470x2 + 1470x2 Combine like terms: 2110x + -2110x = 0 -111 + -2222x + 1470x2 = 0 + -1470x2 + 1470x2 -111 + -2222x + 1470x2 = -1470x2 + 1470x2 Combine like terms: -1470x2 + 1470x2 = 0 -111 + -2222x + 1470x2 = 0 Begin completing the square. Divide all terms by 1470 the coefficient of the squared term: Divide each side by '1470'. -0.07551020408 + -1.511564626x + x2 = 0 Move the constant term to the right: Add '0.07551020408' to each side of the equation. -0.07551020408 + -1.511564626x + 0.07551020408 + x2 = 0 + 0.07551020408 Reorder the terms: -0.07551020408 + 0.07551020408 + -1.511564626x + x2 = 0 + 0.07551020408 Combine like terms: -0.07551020408 + 0.07551020408 = 0.00000000000 0.00000000000 + -1.511564626x + x2 = 0 + 0.07551020408 -1.511564626x + x2 = 0 + 0.07551020408 Combine like terms: 0 + 0.07551020408 = 0.07551020408 -1.511564626x + x2 = 0.07551020408 The x term is -1.511564626x. Take half its coefficient (-0.755782313). Square it (0.5712069046) and add it to both sides. Add '0.5712069046' to each side of the equation. -1.511564626x + 0.5712069046 + x2 = 0.07551020408 + 0.5712069046 Reorder the terms: 0.5712069046 + -1.511564626x + x2 = 0.07551020408 + 0.5712069046 Combine like terms: 0.07551020408 + 0.5712069046 = 0.64671710868 0.5712069046 + -1.511564626x + x2 = 0.64671710868 Factor a perfect square on the left side: (x + -0.755782313)(x + -0.755782313) = 0.64671710868 Calculate the square root of the right side: 0.804187235 Break this problem into two subproblems by setting (x + -0.755782313) equal to 0.804187235 and -0.804187235.Subproblem 1
x + -0.755782313 = 0.804187235 Simplifying x + -0.755782313 = 0.804187235 Reorder the terms: -0.755782313 + x = 0.804187235 Solving -0.755782313 + x = 0.804187235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.755782313' to each side of the equation. -0.755782313 + 0.755782313 + x = 0.804187235 + 0.755782313 Combine like terms: -0.755782313 + 0.755782313 = 0.000000000 0.000000000 + x = 0.804187235 + 0.755782313 x = 0.804187235 + 0.755782313 Combine like terms: 0.804187235 + 0.755782313 = 1.559969548 x = 1.559969548 Simplifying x = 1.559969548Subproblem 2
x + -0.755782313 = -0.804187235 Simplifying x + -0.755782313 = -0.804187235 Reorder the terms: -0.755782313 + x = -0.804187235 Solving -0.755782313 + x = -0.804187235 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.755782313' to each side of the equation. -0.755782313 + 0.755782313 + x = -0.804187235 + 0.755782313 Combine like terms: -0.755782313 + 0.755782313 = 0.000000000 0.000000000 + x = -0.804187235 + 0.755782313 x = -0.804187235 + 0.755782313 Combine like terms: -0.804187235 + 0.755782313 = -0.048404922 x = -0.048404922 Simplifying x = -0.048404922Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.559969548, -0.048404922}
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