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Simplifying 2x2 + -63x + 162 = 0 Reorder the terms: 162 + -63x + 2x2 = 0 Solving 162 + -63x + 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'. 81 + -31.5x + x2 = 0 Move the constant term to the right: Add '-81' to each side of the equation. 81 + -31.5x + -81 + x2 = 0 + -81 Reorder the terms: 81 + -81 + -31.5x + x2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + -31.5x + x2 = 0 + -81 -31.5x + x2 = 0 + -81 Combine like terms: 0 + -81 = -81 -31.5x + x2 = -81 The x term is -31.5x. Take half its coefficient (-15.75). Square it (248.0625) and add it to both sides. Add '248.0625' to each side of the equation. -31.5x + 248.0625 + x2 = -81 + 248.0625 Reorder the terms: 248.0625 + -31.5x + x2 = -81 + 248.0625 Combine like terms: -81 + 248.0625 = 167.0625 248.0625 + -31.5x + x2 = 167.0625 Factor a perfect square on the left side: (x + -15.75)(x + -15.75) = 167.0625 Calculate the square root of the right side: 12.925265955 Break this problem into two subproblems by setting (x + -15.75) equal to 12.925265955 and -12.925265955.Subproblem 1
x + -15.75 = 12.925265955 Simplifying x + -15.75 = 12.925265955 Reorder the terms: -15.75 + x = 12.925265955 Solving -15.75 + x = 12.925265955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.75' to each side of the equation. -15.75 + 15.75 + x = 12.925265955 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + x = 12.925265955 + 15.75 x = 12.925265955 + 15.75 Combine like terms: 12.925265955 + 15.75 = 28.675265955 x = 28.675265955 Simplifying x = 28.675265955Subproblem 2
x + -15.75 = -12.925265955 Simplifying x + -15.75 = -12.925265955 Reorder the terms: -15.75 + x = -12.925265955 Solving -15.75 + x = -12.925265955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15.75' to each side of the equation. -15.75 + 15.75 + x = -12.925265955 + 15.75 Combine like terms: -15.75 + 15.75 = 0.00 0.00 + x = -12.925265955 + 15.75 x = -12.925265955 + 15.75 Combine like terms: -12.925265955 + 15.75 = 2.824734045 x = 2.824734045 Simplifying x = 2.824734045Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.675265955, 2.824734045}
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