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Simplifying x(x + -3) = 1175 Reorder the terms: x(-3 + x) = 1175 (-3 * x + x * x) = 1175 (-3x + x2) = 1175 Solving -3x + x2 = 1175 Solving for variable 'x'. Reorder the terms: -1175 + -3x + x2 = 1175 + -1175 Combine like terms: 1175 + -1175 = 0 -1175 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1175' to each side of the equation. -1175 + -3x + 1175 + x2 = 0 + 1175 Reorder the terms: -1175 + 1175 + -3x + x2 = 0 + 1175 Combine like terms: -1175 + 1175 = 0 0 + -3x + x2 = 0 + 1175 -3x + x2 = 0 + 1175 Combine like terms: 0 + 1175 = 1175 -3x + x2 = 1175 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 = 1175 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 1175 + 2.25 Combine like terms: 1175 + 2.25 = 1177.25 2.25 + -3x + x2 = 1177.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1177.25 Calculate the square root of the right side: 34.311076929 Break this problem into two subproblems by setting (x + -1.5) equal to 34.311076929 and -34.311076929.Subproblem 1
x + -1.5 = 34.311076929 Simplifying x + -1.5 = 34.311076929 Reorder the terms: -1.5 + x = 34.311076929 Solving -1.5 + x = 34.311076929 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 = 34.311076929 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 34.311076929 + 1.5 x = 34.311076929 + 1.5 Combine like terms: 34.311076929 + 1.5 = 35.811076929 x = 35.811076929 Simplifying x = 35.811076929Subproblem 2
x + -1.5 = -34.311076929 Simplifying x + -1.5 = -34.311076929 Reorder the terms: -1.5 + x = -34.311076929 Solving -1.5 + x = -34.311076929 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 = -34.311076929 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -34.311076929 + 1.5 x = -34.311076929 + 1.5 Combine like terms: -34.311076929 + 1.5 = -32.811076929 x = -32.811076929 Simplifying x = -32.811076929Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.811076929, -32.811076929}
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