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Simplifying 2x2 + 29x + -18 = 0 Reorder the terms: -18 + 29x + 2x2 = 0 Solving -18 + 29x + 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'. -9 + 14.5x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 14.5x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 14.5x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 14.5x + x2 = 0 + 9 14.5x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 14.5x + x2 = 9 The x term is 14.5x. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5x + 52.5625 + x2 = 9 + 52.5625 Reorder the terms: 52.5625 + 14.5x + x2 = 9 + 52.5625 Combine like terms: 9 + 52.5625 = 61.5625 52.5625 + 14.5x + x2 = 61.5625 Factor a perfect square on the left side: (x + 7.25)(x + 7.25) = 61.5625 Calculate the square root of the right side: 7.846177413 Break this problem into two subproblems by setting (x + 7.25) equal to 7.846177413 and -7.846177413.Subproblem 1
x + 7.25 = 7.846177413 Simplifying x + 7.25 = 7.846177413 Reorder the terms: 7.25 + x = 7.846177413 Solving 7.25 + x = 7.846177413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = 7.846177413 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 7.846177413 + -7.25 x = 7.846177413 + -7.25 Combine like terms: 7.846177413 + -7.25 = 0.596177413 x = 0.596177413 Simplifying x = 0.596177413Subproblem 2
x + 7.25 = -7.846177413 Simplifying x + 7.25 = -7.846177413 Reorder the terms: 7.25 + x = -7.846177413 Solving 7.25 + x = -7.846177413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = -7.846177413 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -7.846177413 + -7.25 x = -7.846177413 + -7.25 Combine like terms: -7.846177413 + -7.25 = -15.096177413 x = -15.096177413 Simplifying x = -15.096177413Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.596177413, -15.096177413}
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