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Simplifying x * x + 1 + 4x + 3 + 2x * 2x + 3x + -2 = 180 Multiply x * x x2 + 1 + 4x + 3 + 2x * 2x + 3x + -2 = 180 Reorder the terms for easier multiplication: x2 + 1 + 4x + 3 + 2 * 2x * x + 3x + -2 = 180 Multiply 2 * 2 x2 + 1 + 4x + 3 + 4x * x + 3x + -2 = 180 Multiply x * x x2 + 1 + 4x + 3 + 4x2 + 3x + -2 = 180 Reorder the terms: 1 + 3 + -2 + 4x + 3x + x2 + 4x2 = 180 Combine like terms: 1 + 3 = 4 4 + -2 + 4x + 3x + x2 + 4x2 = 180 Combine like terms: 4 + -2 = 2 2 + 4x + 3x + x2 + 4x2 = 180 Combine like terms: 4x + 3x = 7x 2 + 7x + x2 + 4x2 = 180 Combine like terms: x2 + 4x2 = 5x2 2 + 7x + 5x2 = 180 Solving 2 + 7x + 5x2 = 180 Solving for variable 'x'. Reorder the terms: 2 + -180 + 7x + 5x2 = 180 + -180 Combine like terms: 2 + -180 = -178 -178 + 7x + 5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -178 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -35.6 + 1.4x + x2 = 0 Move the constant term to the right: Add '35.6' to each side of the equation. -35.6 + 1.4x + 35.6 + x2 = 0 + 35.6 Reorder the terms: -35.6 + 35.6 + 1.4x + x2 = 0 + 35.6 Combine like terms: -35.6 + 35.6 = 0.0 0.0 + 1.4x + x2 = 0 + 35.6 1.4x + x2 = 0 + 35.6 Combine like terms: 0 + 35.6 = 35.6 1.4x + x2 = 35.6 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 35.6 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 35.6 + 0.49 Combine like terms: 35.6 + 0.49 = 36.09 0.49 + 1.4x + x2 = 36.09 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 36.09 Calculate the square root of the right side: 6.007495318 Break this problem into two subproblems by setting (x + 0.7) equal to 6.007495318 and -6.007495318.Subproblem 1
x + 0.7 = 6.007495318 Simplifying x + 0.7 = 6.007495318 Reorder the terms: 0.7 + x = 6.007495318 Solving 0.7 + x = 6.007495318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 6.007495318 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 6.007495318 + -0.7 x = 6.007495318 + -0.7 Combine like terms: 6.007495318 + -0.7 = 5.307495318 x = 5.307495318 Simplifying x = 5.307495318Subproblem 2
x + 0.7 = -6.007495318 Simplifying x + 0.7 = -6.007495318 Reorder the terms: 0.7 + x = -6.007495318 Solving 0.7 + x = -6.007495318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -6.007495318 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -6.007495318 + -0.7 x = -6.007495318 + -0.7 Combine like terms: -6.007495318 + -0.7 = -6.707495318 x = -6.707495318 Simplifying x = -6.707495318Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.307495318, -6.707495318}
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