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Simplifying 4x2 + 118x = 3x2 + -81 Reorder the terms: 118x + 4x2 = 3x2 + -81 Reorder the terms: 118x + 4x2 = -81 + 3x2 Solving 118x + 4x2 = -81 + 3x2 Solving for variable 'x'. Reorder the terms: 81 + 118x + 4x2 + -3x2 = -81 + 3x2 + 81 + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 81 + 118x + 1x2 = -81 + 3x2 + 81 + -3x2 Reorder the terms: 81 + 118x + 1x2 = -81 + 81 + 3x2 + -3x2 Combine like terms: -81 + 81 = 0 81 + 118x + 1x2 = 0 + 3x2 + -3x2 81 + 118x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 81 + 118x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + 118x + -81 + x2 = 0 + -81 Reorder the terms: 81 + -81 + 118x + x2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + 118x + x2 = 0 + -81 118x + x2 = 0 + -81 Combine like terms: 0 + -81 = -81 118x + x2 = -81 The x term is 118x. Take half its coefficient (59). Square it (3481) and add it to both sides. Add '3481' to each side of the equation. 118x + 3481 + x2 = -81 + 3481 Reorder the terms: 3481 + 118x + x2 = -81 + 3481 Combine like terms: -81 + 3481 = 3400 3481 + 118x + x2 = 3400 Factor a perfect square on the left side: (x + 59)(x + 59) = 3400 Calculate the square root of the right side: 58.309518948 Break this problem into two subproblems by setting (x + 59) equal to 58.309518948 and -58.309518948.Subproblem 1
x + 59 = 58.309518948 Simplifying x + 59 = 58.309518948 Reorder the terms: 59 + x = 58.309518948 Solving 59 + x = 58.309518948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-59' to each side of the equation. 59 + -59 + x = 58.309518948 + -59 Combine like terms: 59 + -59 = 0 0 + x = 58.309518948 + -59 x = 58.309518948 + -59 Combine like terms: 58.309518948 + -59 = -0.690481052 x = -0.690481052 Simplifying x = -0.690481052Subproblem 2
x + 59 = -58.309518948 Simplifying x + 59 = -58.309518948 Reorder the terms: 59 + x = -58.309518948 Solving 59 + x = -58.309518948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-59' to each side of the equation. 59 + -59 + x = -58.309518948 + -59 Combine like terms: 59 + -59 = 0 0 + x = -58.309518948 + -59 x = -58.309518948 + -59 Combine like terms: -58.309518948 + -59 = -117.309518948 x = -117.309518948 Simplifying x = -117.309518948Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.690481052, -117.309518948}
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