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Simplifying 18x2 + 18x + -343 = 0 Reorder the terms: -343 + 18x + 18x2 = 0 Solving -343 + 18x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -19.05555556 + x + x2 = 0 Move the constant term to the right: Add '19.05555556' to each side of the equation. -19.05555556 + x + 19.05555556 + x2 = 0 + 19.05555556 Reorder the terms: -19.05555556 + 19.05555556 + x + x2 = 0 + 19.05555556 Combine like terms: -19.05555556 + 19.05555556 = 0.00000000 0.00000000 + x + x2 = 0 + 19.05555556 x + x2 = 0 + 19.05555556 Combine like terms: 0 + 19.05555556 = 19.05555556 x + x2 = 19.05555556 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 19.05555556 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 19.05555556 + 0.25 Combine like terms: 19.05555556 + 0.25 = 19.30555556 1.25 + x2 = 19.30555556 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 19.30555556 Calculate the square root of the right side: 4.393808776 Break this problem into two subproblems by setting (x + 0.5) equal to 4.393808776 and -4.393808776.Subproblem 1
x + 0.5 = 4.393808776 Simplifying x + 0.5 = 4.393808776 Reorder the terms: 0.5 + x = 4.393808776 Solving 0.5 + x = 4.393808776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.393808776 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.393808776 + -0.5 x = 4.393808776 + -0.5 Combine like terms: 4.393808776 + -0.5 = 3.893808776 x = 3.893808776 Simplifying x = 3.893808776Subproblem 2
x + 0.5 = -4.393808776 Simplifying x + 0.5 = -4.393808776 Reorder the terms: 0.5 + x = -4.393808776 Solving 0.5 + x = -4.393808776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.393808776 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.393808776 + -0.5 x = -4.393808776 + -0.5 Combine like terms: -4.393808776 + -0.5 = -4.893808776 x = -4.893808776 Simplifying x = -4.893808776Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.893808776, -4.893808776}
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