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Simplifying 30x + (x2 + 40x) + 10x + 35 = 180 Reorder the terms: 30x + (40x + x2) + 10x + 35 = 180 Remove parenthesis around (40x + x2) 30x + 40x + x2 + 10x + 35 = 180 Reorder the terms: 35 + 30x + 40x + 10x + x2 = 180 Combine like terms: 30x + 40x = 70x 35 + 70x + 10x + x2 = 180 Combine like terms: 70x + 10x = 80x 35 + 80x + x2 = 180 Solving 35 + 80x + x2 = 180 Solving for variable 'x'. Reorder the terms: 35 + -180 + 80x + x2 = 180 + -180 Combine like terms: 35 + -180 = -145 -145 + 80x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -145 + 80x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '145' to each side of the equation. -145 + 80x + 145 + x2 = 0 + 145 Reorder the terms: -145 + 145 + 80x + x2 = 0 + 145 Combine like terms: -145 + 145 = 0 0 + 80x + x2 = 0 + 145 80x + x2 = 0 + 145 Combine like terms: 0 + 145 = 145 80x + x2 = 145 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = 145 + 1600 Reorder the terms: 1600 + 80x + x2 = 145 + 1600 Combine like terms: 145 + 1600 = 1745 1600 + 80x + x2 = 1745 Factor a perfect square on the left side: (x + 40)(x + 40) = 1745 Calculate the square root of the right side: 41.773197148 Break this problem into two subproblems by setting (x + 40) equal to 41.773197148 and -41.773197148.Subproblem 1
x + 40 = 41.773197148 Simplifying x + 40 = 41.773197148 Reorder the terms: 40 + x = 41.773197148 Solving 40 + x = 41.773197148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 41.773197148 + -40 Combine like terms: 40 + -40 = 0 0 + x = 41.773197148 + -40 x = 41.773197148 + -40 Combine like terms: 41.773197148 + -40 = 1.773197148 x = 1.773197148 Simplifying x = 1.773197148Subproblem 2
x + 40 = -41.773197148 Simplifying x + 40 = -41.773197148 Reorder the terms: 40 + x = -41.773197148 Solving 40 + x = -41.773197148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -41.773197148 + -40 Combine like terms: 40 + -40 = 0 0 + x = -41.773197148 + -40 x = -41.773197148 + -40 Combine like terms: -41.773197148 + -40 = -81.773197148 x = -81.773197148 Simplifying x = -81.773197148Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.773197148, -81.773197148}
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