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Simplifying x2 + 2x + x + 70 = 180 Reorder the terms: 70 + 2x + x + x2 = 180 Combine like terms: 2x + x = 3x 70 + 3x + x2 = 180 Solving 70 + 3x + x2 = 180 Solving for variable 'x'. Reorder the terms: 70 + -180 + 3x + x2 = 180 + -180 Combine like terms: 70 + -180 = -110 -110 + 3x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -110 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + 3x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 3x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 3x + x2 = 0 + 110 3x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 3x + x2 = 110 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 110 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 110 + 2.25 Combine like terms: 110 + 2.25 = 112.25 2.25 + 3x + x2 = 112.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 112.25 Calculate the square root of the right side: 10.59481005 Break this problem into two subproblems by setting (x + 1.5) equal to 10.59481005 and -10.59481005.Subproblem 1
x + 1.5 = 10.59481005 Simplifying x + 1.5 = 10.59481005 Reorder the terms: 1.5 + x = 10.59481005 Solving 1.5 + x = 10.59481005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 10.59481005 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.59481005 + -1.5 x = 10.59481005 + -1.5 Combine like terms: 10.59481005 + -1.5 = 9.09481005 x = 9.09481005 Simplifying x = 9.09481005Subproblem 2
x + 1.5 = -10.59481005 Simplifying x + 1.5 = -10.59481005 Reorder the terms: 1.5 + x = -10.59481005 Solving 1.5 + x = -10.59481005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -10.59481005 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.59481005 + -1.5 x = -10.59481005 + -1.5 Combine like terms: -10.59481005 + -1.5 = -12.09481005 x = -12.09481005 Simplifying x = -12.09481005Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.09481005, -12.09481005}
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