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Simplifying 2x(-9 + -1x) = -13 (-9 * 2x + -1x * 2x) = -13 (-18x + -2x2) = -13 Solving -18x + -2x2 = -13 Solving for variable 'x'. Reorder the terms: 13 + -18x + -2x2 = -13 + 13 Combine like terms: -13 + 13 = 0 13 + -18x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6.5 + 9x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 9x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 9x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 9x + x2 = 0 + 6.5 9x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 9x + x2 = 6.5 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 = 6.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 6.5 + 20.25 Combine like terms: 6.5 + 20.25 = 26.75 20.25 + 9x + x2 = 26.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 26.75 Calculate the square root of the right side: 5.172040216 Break this problem into two subproblems by setting (x + 4.5) equal to 5.172040216 and -5.172040216.Subproblem 1
x + 4.5 = 5.172040216 Simplifying x + 4.5 = 5.172040216 Reorder the terms: 4.5 + x = 5.172040216 Solving 4.5 + x = 5.172040216 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 = 5.172040216 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.172040216 + -4.5 x = 5.172040216 + -4.5 Combine like terms: 5.172040216 + -4.5 = 0.672040216 x = 0.672040216 Simplifying x = 0.672040216Subproblem 2
x + 4.5 = -5.172040216 Simplifying x + 4.5 = -5.172040216 Reorder the terms: 4.5 + x = -5.172040216 Solving 4.5 + x = -5.172040216 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 = -5.172040216 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.172040216 + -4.5 x = -5.172040216 + -4.5 Combine like terms: -5.172040216 + -4.5 = -9.672040216 x = -9.672040216 Simplifying x = -9.672040216Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.672040216, -9.672040216}
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