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Simplifying x2 + 4x + -147 = 0 Reorder the terms: -147 + 4x + x2 = 0 Solving -147 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '147' to each side of the equation. -147 + 4x + 147 + x2 = 0 + 147 Reorder the terms: -147 + 147 + 4x + x2 = 0 + 147 Combine like terms: -147 + 147 = 0 0 + 4x + x2 = 0 + 147 4x + x2 = 0 + 147 Combine like terms: 0 + 147 = 147 4x + x2 = 147 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 147 + 4 Reorder the terms: 4 + 4x + x2 = 147 + 4 Combine like terms: 147 + 4 = 151 4 + 4x + x2 = 151 Factor a perfect square on the left side: (x + 2)(x + 2) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (x + 2) equal to 12.288205727 and -12.288205727.Subproblem 1
x + 2 = 12.288205727 Simplifying x + 2 = 12.288205727 Reorder the terms: 2 + x = 12.288205727 Solving 2 + x = 12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 12.288205727 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.288205727 + -2 x = 12.288205727 + -2 Combine like terms: 12.288205727 + -2 = 10.288205727 x = 10.288205727 Simplifying x = 10.288205727Subproblem 2
x + 2 = -12.288205727 Simplifying x + 2 = -12.288205727 Reorder the terms: 2 + x = -12.288205727 Solving 2 + x = -12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -12.288205727 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.288205727 + -2 x = -12.288205727 + -2 Combine like terms: -12.288205727 + -2 = -14.288205727 x = -14.288205727 Simplifying x = -14.288205727Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.288205727, -14.288205727}
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