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Simplifying (x2 + 3x) = 150 Reorder the terms: (3x + x2) = 150 Remove parenthesis around (3x + x2) 3x + x2 = 150 Solving 3x + x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 3x + x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + 3x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 3x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 3x + x2 = 0 + 150 3x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 3x + x2 = 150 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 = 150 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 150 + 2.25 Combine like terms: 150 + 2.25 = 152.25 2.25 + 3x + x2 = 152.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 152.25 Calculate the square root of the right side: 12.338962679 Break this problem into two subproblems by setting (x + 1.5) equal to 12.338962679 and -12.338962679.Subproblem 1
x + 1.5 = 12.338962679 Simplifying x + 1.5 = 12.338962679 Reorder the terms: 1.5 + x = 12.338962679 Solving 1.5 + x = 12.338962679 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 = 12.338962679 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.338962679 + -1.5 x = 12.338962679 + -1.5 Combine like terms: 12.338962679 + -1.5 = 10.838962679 x = 10.838962679 Simplifying x = 10.838962679Subproblem 2
x + 1.5 = -12.338962679 Simplifying x + 1.5 = -12.338962679 Reorder the terms: 1.5 + x = -12.338962679 Solving 1.5 + x = -12.338962679 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 = -12.338962679 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.338962679 + -1.5 x = -12.338962679 + -1.5 Combine like terms: -12.338962679 + -1.5 = -13.838962679 x = -13.838962679 Simplifying x = -13.838962679Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.838962679, -13.838962679}
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