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Simplifying x2 + 3x + 7(3x + -1) = 0 Reorder the terms: x2 + 3x + 7(-1 + 3x) = 0 x2 + 3x + (-1 * 7 + 3x * 7) = 0 x2 + 3x + (-7 + 21x) = 0 Reorder the terms: -7 + 3x + 21x + x2 = 0 Combine like terms: 3x + 21x = 24x -7 + 24x + x2 = 0 Solving -7 + 24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 24x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 24x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 24x + x2 = 0 + 7 24x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 24x + x2 = 7 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 7 + 144 Reorder the terms: 144 + 24x + x2 = 7 + 144 Combine like terms: 7 + 144 = 151 144 + 24x + x2 = 151 Factor a perfect square on the left side: (x + 12)(x + 12) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (x + 12) equal to 12.288205727 and -12.288205727.Subproblem 1
x + 12 = 12.288205727 Simplifying x + 12 = 12.288205727 Reorder the terms: 12 + x = 12.288205727 Solving 12 + x = 12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 12.288205727 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.288205727 + -12 x = 12.288205727 + -12 Combine like terms: 12.288205727 + -12 = 0.288205727 x = 0.288205727 Simplifying x = 0.288205727Subproblem 2
x + 12 = -12.288205727 Simplifying x + 12 = -12.288205727 Reorder the terms: 12 + x = -12.288205727 Solving 12 + x = -12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -12.288205727 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.288205727 + -12 x = -12.288205727 + -12 Combine like terms: -12.288205727 + -12 = -24.288205727 x = -24.288205727 Simplifying x = -24.288205727Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.288205727, -24.288205727}
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