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Simplifying 42x2 + 11x + -18 = 0 Reorder the terms: -18 + 11x + 42x2 = 0 Solving -18 + 11x + 42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -0.4285714286 + 0.2619047619x + x2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.2619047619x + 0.4285714286 + x2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + 0.2619047619x + x2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + 0.2619047619x + x2 = 0 + 0.4285714286 0.2619047619x + x2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 0.2619047619x + x2 = 0.4285714286 The x term is 0.2619047619x. Take half its coefficient (0.130952381). Square it (0.01714852609) and add it to both sides. Add '0.01714852609' to each side of the equation. 0.2619047619x + 0.01714852609 + x2 = 0.4285714286 + 0.01714852609 Reorder the terms: 0.01714852609 + 0.2619047619x + x2 = 0.4285714286 + 0.01714852609 Combine like terms: 0.4285714286 + 0.01714852609 = 0.44571995469 0.01714852609 + 0.2619047619x + x2 = 0.44571995469 Factor a perfect square on the left side: (x + 0.130952381)(x + 0.130952381) = 0.44571995469 Calculate the square root of the right side: 0.667622614 Break this problem into two subproblems by setting (x + 0.130952381) equal to 0.667622614 and -0.667622614.Subproblem 1
x + 0.130952381 = 0.667622614 Simplifying x + 0.130952381 = 0.667622614 Reorder the terms: 0.130952381 + x = 0.667622614 Solving 0.130952381 + x = 0.667622614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.130952381' to each side of the equation. 0.130952381 + -0.130952381 + x = 0.667622614 + -0.130952381 Combine like terms: 0.130952381 + -0.130952381 = 0.000000000 0.000000000 + x = 0.667622614 + -0.130952381 x = 0.667622614 + -0.130952381 Combine like terms: 0.667622614 + -0.130952381 = 0.536670233 x = 0.536670233 Simplifying x = 0.536670233Subproblem 2
x + 0.130952381 = -0.667622614 Simplifying x + 0.130952381 = -0.667622614 Reorder the terms: 0.130952381 + x = -0.667622614 Solving 0.130952381 + x = -0.667622614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.130952381' to each side of the equation. 0.130952381 + -0.130952381 + x = -0.667622614 + -0.130952381 Combine like terms: 0.130952381 + -0.130952381 = 0.000000000 0.000000000 + x = -0.667622614 + -0.130952381 x = -0.667622614 + -0.130952381 Combine like terms: -0.667622614 + -0.130952381 = -0.798574995 x = -0.798574995 Simplifying x = -0.798574995Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.536670233, -0.798574995}
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