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Simplifying x2 + 3x = 177 Reorder the terms: 3x + x2 = 177 Solving 3x + x2 = 177 Solving for variable 'x'. Reorder the terms: -177 + 3x + x2 = 177 + -177 Combine like terms: 177 + -177 = 0 -177 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '177' to each side of the equation. -177 + 3x + 177 + x2 = 0 + 177 Reorder the terms: -177 + 177 + 3x + x2 = 0 + 177 Combine like terms: -177 + 177 = 0 0 + 3x + x2 = 0 + 177 3x + x2 = 0 + 177 Combine like terms: 0 + 177 = 177 3x + x2 = 177 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 = 177 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 177 + 2.25 Combine like terms: 177 + 2.25 = 179.25 2.25 + 3x + x2 = 179.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 179.25 Calculate the square root of the right side: 13.388427839 Break this problem into two subproblems by setting (x + 1.5) equal to 13.388427839 and -13.388427839.Subproblem 1
x + 1.5 = 13.388427839 Simplifying x + 1.5 = 13.388427839 Reorder the terms: 1.5 + x = 13.388427839 Solving 1.5 + x = 13.388427839 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 = 13.388427839 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 13.388427839 + -1.5 x = 13.388427839 + -1.5 Combine like terms: 13.388427839 + -1.5 = 11.888427839 x = 11.888427839 Simplifying x = 11.888427839Subproblem 2
x + 1.5 = -13.388427839 Simplifying x + 1.5 = -13.388427839 Reorder the terms: 1.5 + x = -13.388427839 Solving 1.5 + x = -13.388427839 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 = -13.388427839 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -13.388427839 + -1.5 x = -13.388427839 + -1.5 Combine like terms: -13.388427839 + -1.5 = -14.888427839 x = -14.888427839 Simplifying x = -14.888427839Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.888427839, -14.888427839}
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