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Simplifying 7x + (3x + -5)(8x + 5) = 180 Reorder the terms: 7x + (-5 + 3x)(8x + 5) = 180 Reorder the terms: 7x + (-5 + 3x)(5 + 8x) = 180 Multiply (-5 + 3x) * (5 + 8x) 7x + (-5(5 + 8x) + 3x * (5 + 8x)) = 180 7x + ((5 * -5 + 8x * -5) + 3x * (5 + 8x)) = 180 7x + ((-25 + -40x) + 3x * (5 + 8x)) = 180 7x + (-25 + -40x + (5 * 3x + 8x * 3x)) = 180 7x + (-25 + -40x + (15x + 24x2)) = 180 Combine like terms: -40x + 15x = -25x 7x + (-25 + -25x + 24x2) = 180 Reorder the terms: -25 + 7x + -25x + 24x2 = 180 Combine like terms: 7x + -25x = -18x -25 + -18x + 24x2 = 180 Solving -25 + -18x + 24x2 = 180 Solving for variable 'x'. Reorder the terms: -25 + -180 + -18x + 24x2 = 180 + -180 Combine like terms: -25 + -180 = -205 -205 + -18x + 24x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -205 + -18x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -8.541666667 + -0.75x + x2 = 0 Move the constant term to the right: Add '8.541666667' to each side of the equation. -8.541666667 + -0.75x + 8.541666667 + x2 = 0 + 8.541666667 Reorder the terms: -8.541666667 + 8.541666667 + -0.75x + x2 = 0 + 8.541666667 Combine like terms: -8.541666667 + 8.541666667 = 0.000000000 0.000000000 + -0.75x + x2 = 0 + 8.541666667 -0.75x + x2 = 0 + 8.541666667 Combine like terms: 0 + 8.541666667 = 8.541666667 -0.75x + x2 = 8.541666667 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 8.541666667 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 8.541666667 + 0.140625 Combine like terms: 8.541666667 + 0.140625 = 8.682291667 0.140625 + -0.75x + x2 = 8.682291667 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 8.682291667 Calculate the square root of the right side: 2.946572868 Break this problem into two subproblems by setting (x + -0.375) equal to 2.946572868 and -2.946572868.Subproblem 1
x + -0.375 = 2.946572868 Simplifying x + -0.375 = 2.946572868 Reorder the terms: -0.375 + x = 2.946572868 Solving -0.375 + x = 2.946572868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 2.946572868 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 2.946572868 + 0.375 x = 2.946572868 + 0.375 Combine like terms: 2.946572868 + 0.375 = 3.321572868 x = 3.321572868 Simplifying x = 3.321572868Subproblem 2
x + -0.375 = -2.946572868 Simplifying x + -0.375 = -2.946572868 Reorder the terms: -0.375 + x = -2.946572868 Solving -0.375 + x = -2.946572868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -2.946572868 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -2.946572868 + 0.375 x = -2.946572868 + 0.375 Combine like terms: -2.946572868 + 0.375 = -2.571572868 x = -2.571572868 Simplifying x = -2.571572868Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.321572868, -2.571572868}
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