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Simplifying 2x2 + -7x + 3 = 180 Reorder the terms: 3 + -7x + 2x2 = 180 Solving 3 + -7x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 3 + -180 + -7x + 2x2 = 180 + -180 Combine like terms: 3 + -180 = -177 -177 + -7x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -177 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -88.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '88.5' to each side of the equation. -88.5 + -3.5x + 88.5 + x2 = 0 + 88.5 Reorder the terms: -88.5 + 88.5 + -3.5x + x2 = 0 + 88.5 Combine like terms: -88.5 + 88.5 = 0.0 0.0 + -3.5x + x2 = 0 + 88.5 -3.5x + x2 = 0 + 88.5 Combine like terms: 0 + 88.5 = 88.5 -3.5x + x2 = 88.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 88.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 88.5 + 3.0625 Combine like terms: 88.5 + 3.0625 = 91.5625 3.0625 + -3.5x + x2 = 91.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 91.5625 Calculate the square root of the right side: 9.568829605 Break this problem into two subproblems by setting (x + -1.75) equal to 9.568829605 and -9.568829605.Subproblem 1
x + -1.75 = 9.568829605 Simplifying x + -1.75 = 9.568829605 Reorder the terms: -1.75 + x = 9.568829605 Solving -1.75 + x = 9.568829605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 9.568829605 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 9.568829605 + 1.75 x = 9.568829605 + 1.75 Combine like terms: 9.568829605 + 1.75 = 11.318829605 x = 11.318829605 Simplifying x = 11.318829605Subproblem 2
x + -1.75 = -9.568829605 Simplifying x + -1.75 = -9.568829605 Reorder the terms: -1.75 + x = -9.568829605 Solving -1.75 + x = -9.568829605 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -9.568829605 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -9.568829605 + 1.75 x = -9.568829605 + 1.75 Combine like terms: -9.568829605 + 1.75 = -7.818829605 x = -7.818829605 Simplifying x = -7.818829605Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.318829605, -7.818829605}
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