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Simplifying x(2x + 4) + (3x + -5) = 137 Reorder the terms: x(4 + 2x) + (3x + -5) = 137 (4 * x + 2x * x) + (3x + -5) = 137 (4x + 2x2) + (3x + -5) = 137 Reorder the terms: 4x + 2x2 + (-5 + 3x) = 137 Remove parenthesis around (-5 + 3x) 4x + 2x2 + -5 + 3x = 137 Reorder the terms: -5 + 4x + 3x + 2x2 = 137 Combine like terms: 4x + 3x = 7x -5 + 7x + 2x2 = 137 Solving -5 + 7x + 2x2 = 137 Solving for variable 'x'. Reorder the terms: -5 + -137 + 7x + 2x2 = 137 + -137 Combine like terms: -5 + -137 = -142 -142 + 7x + 2x2 = 137 + -137 Combine like terms: 137 + -137 = 0 -142 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -71 + 3.5x + x2 = 0 Move the constant term to the right: Add '71' to each side of the equation. -71 + 3.5x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + 3.5x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + 3.5x + x2 = 0 + 71 3.5x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 3.5x + x2 = 71 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 71 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 71 + 3.0625 Combine like terms: 71 + 3.0625 = 74.0625 3.0625 + 3.5x + x2 = 74.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 74.0625 Calculate the square root of the right side: 8.605957239 Break this problem into two subproblems by setting (x + 1.75) equal to 8.605957239 and -8.605957239.Subproblem 1
x + 1.75 = 8.605957239 Simplifying x + 1.75 = 8.605957239 Reorder the terms: 1.75 + x = 8.605957239 Solving 1.75 + x = 8.605957239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 8.605957239 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 8.605957239 + -1.75 x = 8.605957239 + -1.75 Combine like terms: 8.605957239 + -1.75 = 6.855957239 x = 6.855957239 Simplifying x = 6.855957239Subproblem 2
x + 1.75 = -8.605957239 Simplifying x + 1.75 = -8.605957239 Reorder the terms: 1.75 + x = -8.605957239 Solving 1.75 + x = -8.605957239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -8.605957239 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -8.605957239 + -1.75 x = -8.605957239 + -1.75 Combine like terms: -8.605957239 + -1.75 = -10.355957239 x = -10.355957239 Simplifying x = -10.355957239Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.855957239, -10.355957239}
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