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Simplifying 1.33x2 + 2x + -18 = 0 Reorder the terms: -18 + 2x + 1.33x2 = 0 Solving -18 + 2x + 1.33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.33 the coefficient of the squared term: Divide each side by '1.33'. -13.53383459 + 1.503759398x + x2 = 0 Move the constant term to the right: Add '13.53383459' to each side of the equation. -13.53383459 + 1.503759398x + 13.53383459 + x2 = 0 + 13.53383459 Reorder the terms: -13.53383459 + 13.53383459 + 1.503759398x + x2 = 0 + 13.53383459 Combine like terms: -13.53383459 + 13.53383459 = 0.00000000 0.00000000 + 1.503759398x + x2 = 0 + 13.53383459 1.503759398x + x2 = 0 + 13.53383459 Combine like terms: 0 + 13.53383459 = 13.53383459 1.503759398x + x2 = 13.53383459 The x term is 1.503759398x. Take half its coefficient (0.751879699). Square it (0.5653230818) and add it to both sides. Add '0.5653230818' to each side of the equation. 1.503759398x + 0.5653230818 + x2 = 13.53383459 + 0.5653230818 Reorder the terms: 0.5653230818 + 1.503759398x + x2 = 13.53383459 + 0.5653230818 Combine like terms: 13.53383459 + 0.5653230818 = 14.0991576718 0.5653230818 + 1.503759398x + x2 = 14.0991576718 Factor a perfect square on the left side: (x + 0.751879699)(x + 0.751879699) = 14.0991576718 Calculate the square root of the right side: 3.754884508 Break this problem into two subproblems by setting (x + 0.751879699) equal to 3.754884508 and -3.754884508.Subproblem 1
x + 0.751879699 = 3.754884508 Simplifying x + 0.751879699 = 3.754884508 Reorder the terms: 0.751879699 + x = 3.754884508 Solving 0.751879699 + x = 3.754884508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.751879699' to each side of the equation. 0.751879699 + -0.751879699 + x = 3.754884508 + -0.751879699 Combine like terms: 0.751879699 + -0.751879699 = 0.000000000 0.000000000 + x = 3.754884508 + -0.751879699 x = 3.754884508 + -0.751879699 Combine like terms: 3.754884508 + -0.751879699 = 3.003004809 x = 3.003004809 Simplifying x = 3.003004809Subproblem 2
x + 0.751879699 = -3.754884508 Simplifying x + 0.751879699 = -3.754884508 Reorder the terms: 0.751879699 + x = -3.754884508 Solving 0.751879699 + x = -3.754884508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.751879699' to each side of the equation. 0.751879699 + -0.751879699 + x = -3.754884508 + -0.751879699 Combine like terms: 0.751879699 + -0.751879699 = 0.000000000 0.000000000 + x = -3.754884508 + -0.751879699 x = -3.754884508 + -0.751879699 Combine like terms: -3.754884508 + -0.751879699 = -4.506764207 x = -4.506764207 Simplifying x = -4.506764207Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.003004809, -4.506764207}
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