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Simplifying x * x + 2x + -150 = 0 Multiply x * x x2 + 2x + -150 = 0 Reorder the terms: -150 + 2x + x2 = 0 Solving -150 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '150' to each side of the equation. -150 + 2x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 2x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 2x + x2 = 0 + 150 2x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 2x + x2 = 150 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 150 + 1 Reorder the terms: 1 + 2x + x2 = 150 + 1 Combine like terms: 150 + 1 = 151 1 + 2x + x2 = 151 Factor a perfect square on the left side: (x + 1)(x + 1) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (x + 1) equal to 12.288205727 and -12.288205727.Subproblem 1
x + 1 = 12.288205727 Simplifying x + 1 = 12.288205727 Reorder the terms: 1 + x = 12.288205727 Solving 1 + x = 12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 12.288205727 + -1 Combine like terms: 1 + -1 = 0 0 + x = 12.288205727 + -1 x = 12.288205727 + -1 Combine like terms: 12.288205727 + -1 = 11.288205727 x = 11.288205727 Simplifying x = 11.288205727Subproblem 2
x + 1 = -12.288205727 Simplifying x + 1 = -12.288205727 Reorder the terms: 1 + x = -12.288205727 Solving 1 + x = -12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -12.288205727 + -1 Combine like terms: 1 + -1 = 0 0 + x = -12.288205727 + -1 x = -12.288205727 + -1 Combine like terms: -12.288205727 + -1 = -13.288205727 x = -13.288205727 Simplifying x = -13.288205727Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.288205727, -13.288205727}
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