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Simplifying 3x2 + 6x + -143 = 0 Reorder the terms: -143 + 6x + 3x2 = 0 Solving -143 + 6x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -47.66666667 + 2x + x2 = 0 Move the constant term to the right: Add '47.66666667' to each side of the equation. -47.66666667 + 2x + 47.66666667 + x2 = 0 + 47.66666667 Reorder the terms: -47.66666667 + 47.66666667 + 2x + x2 = 0 + 47.66666667 Combine like terms: -47.66666667 + 47.66666667 = 0.00000000 0.00000000 + 2x + x2 = 0 + 47.66666667 2x + x2 = 0 + 47.66666667 Combine like terms: 0 + 47.66666667 = 47.66666667 2x + x2 = 47.66666667 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 = 47.66666667 + 1 Reorder the terms: 1 + 2x + x2 = 47.66666667 + 1 Combine like terms: 47.66666667 + 1 = 48.66666667 1 + 2x + x2 = 48.66666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 48.66666667 Calculate the square root of the right side: 6.976149846 Break this problem into two subproblems by setting (x + 1) equal to 6.976149846 and -6.976149846.Subproblem 1
x + 1 = 6.976149846 Simplifying x + 1 = 6.976149846 Reorder the terms: 1 + x = 6.976149846 Solving 1 + x = 6.976149846 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 = 6.976149846 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.976149846 + -1 x = 6.976149846 + -1 Combine like terms: 6.976149846 + -1 = 5.976149846 x = 5.976149846 Simplifying x = 5.976149846Subproblem 2
x + 1 = -6.976149846 Simplifying x + 1 = -6.976149846 Reorder the terms: 1 + x = -6.976149846 Solving 1 + x = -6.976149846 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 = -6.976149846 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.976149846 + -1 x = -6.976149846 + -1 Combine like terms: -6.976149846 + -1 = -7.976149846 x = -7.976149846 Simplifying x = -7.976149846Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.976149846, -7.976149846}
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