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Simplifying 2x2 + -9x + -280 = 180 Reorder the terms: -280 + -9x + 2x2 = 180 Solving -280 + -9x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -280 + -180 + -9x + 2x2 = 180 + -180 Combine like terms: -280 + -180 = -460 -460 + -9x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -460 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -230 + -4.5x + x2 = 0 Move the constant term to the right: Add '230' to each side of the equation. -230 + -4.5x + 230 + x2 = 0 + 230 Reorder the terms: -230 + 230 + -4.5x + x2 = 0 + 230 Combine like terms: -230 + 230 = 0 0 + -4.5x + x2 = 0 + 230 -4.5x + x2 = 0 + 230 Combine like terms: 0 + 230 = 230 -4.5x + x2 = 230 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 230 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 230 + 5.0625 Combine like terms: 230 + 5.0625 = 235.0625 5.0625 + -4.5x + x2 = 235.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 235.0625 Calculate the square root of the right side: 15.331748106 Break this problem into two subproblems by setting (x + -2.25) equal to 15.331748106 and -15.331748106.Subproblem 1
x + -2.25 = 15.331748106 Simplifying x + -2.25 = 15.331748106 Reorder the terms: -2.25 + x = 15.331748106 Solving -2.25 + x = 15.331748106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 15.331748106 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 15.331748106 + 2.25 x = 15.331748106 + 2.25 Combine like terms: 15.331748106 + 2.25 = 17.581748106 x = 17.581748106 Simplifying x = 17.581748106Subproblem 2
x + -2.25 = -15.331748106 Simplifying x + -2.25 = -15.331748106 Reorder the terms: -2.25 + x = -15.331748106 Solving -2.25 + x = -15.331748106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -15.331748106 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -15.331748106 + 2.25 x = -15.331748106 + 2.25 Combine like terms: -15.331748106 + 2.25 = -13.081748106 x = -13.081748106 Simplifying x = -13.081748106Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.581748106, -13.081748106}
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