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Simplifying x(2x + -18) + -143 = 0 Reorder the terms: x(-18 + 2x) + -143 = 0 (-18 * x + 2x * x) + -143 = 0 (-18x + 2x2) + -143 = 0 Reorder the terms: -143 + -18x + 2x2 = 0 Solving -143 + -18x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -71.5 + -9x + x2 = 0 Move the constant term to the right: Add '71.5' to each side of the equation. -71.5 + -9x + 71.5 + x2 = 0 + 71.5 Reorder the terms: -71.5 + 71.5 + -9x + x2 = 0 + 71.5 Combine like terms: -71.5 + 71.5 = 0.0 0.0 + -9x + x2 = 0 + 71.5 -9x + x2 = 0 + 71.5 Combine like terms: 0 + 71.5 = 71.5 -9x + x2 = 71.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 71.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 71.5 + 20.25 Combine like terms: 71.5 + 20.25 = 91.75 20.25 + -9x + x2 = 91.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 91.75 Calculate the square root of the right side: 9.57862203 Break this problem into two subproblems by setting (x + -4.5) equal to 9.57862203 and -9.57862203.Subproblem 1
x + -4.5 = 9.57862203 Simplifying x + -4.5 = 9.57862203 Reorder the terms: -4.5 + x = 9.57862203 Solving -4.5 + x = 9.57862203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 9.57862203 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 9.57862203 + 4.5 x = 9.57862203 + 4.5 Combine like terms: 9.57862203 + 4.5 = 14.07862203 x = 14.07862203 Simplifying x = 14.07862203Subproblem 2
x + -4.5 = -9.57862203 Simplifying x + -4.5 = -9.57862203 Reorder the terms: -4.5 + x = -9.57862203 Solving -4.5 + x = -9.57862203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -9.57862203 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -9.57862203 + 4.5 x = -9.57862203 + 4.5 Combine like terms: -9.57862203 + 4.5 = -5.07862203 x = -5.07862203 Simplifying x = -5.07862203Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.07862203, -5.07862203}
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