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Simplifying 2x2 + -6x + 3 + -4x + -18x2 = 0 Reorder the terms: 3 + -6x + -4x + 2x2 + -18x2 = 0 Combine like terms: -6x + -4x = -10x 3 + -10x + 2x2 + -18x2 = 0 Combine like terms: 2x2 + -18x2 = -16x2 3 + -10x + -16x2 = 0 Solving 3 + -10x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.1875 + 0.625x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + 0.625x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + 0.625x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + 0.625x + x2 = 0 + 0.1875 0.625x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 0.625x + x2 = 0.1875 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 0.1875 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 0.1875 + 0.09765625 Combine like terms: 0.1875 + 0.09765625 = 0.28515625 0.09765625 + 0.625x + x2 = 0.28515625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 0.28515625 Calculate the square root of the right side: 0.534000234 Break this problem into two subproblems by setting (x + 0.3125) equal to 0.534000234 and -0.534000234.Subproblem 1
x + 0.3125 = 0.534000234 Simplifying x + 0.3125 = 0.534000234 Reorder the terms: 0.3125 + x = 0.534000234 Solving 0.3125 + x = 0.534000234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 0.534000234 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 0.534000234 + -0.3125 x = 0.534000234 + -0.3125 Combine like terms: 0.534000234 + -0.3125 = 0.221500234 x = 0.221500234 Simplifying x = 0.221500234Subproblem 2
x + 0.3125 = -0.534000234 Simplifying x + 0.3125 = -0.534000234 Reorder the terms: 0.3125 + x = -0.534000234 Solving 0.3125 + x = -0.534000234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -0.534000234 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -0.534000234 + -0.3125 x = -0.534000234 + -0.3125 Combine like terms: -0.534000234 + -0.3125 = -0.846500234 x = -0.846500234 Simplifying x = -0.846500234Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.221500234, -0.846500234}
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