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Simplifying 2x2 + -59x + -84 = 0 Reorder the terms: -84 + -59x + 2x2 = 0 Solving -84 + -59x + 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'. -42 + -29.5x + x2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + -29.5x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -29.5x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -29.5x + x2 = 0 + 42 -29.5x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -29.5x + x2 = 42 The x term is -29.5x. Take half its coefficient (-14.75). Square it (217.5625) and add it to both sides. Add '217.5625' to each side of the equation. -29.5x + 217.5625 + x2 = 42 + 217.5625 Reorder the terms: 217.5625 + -29.5x + x2 = 42 + 217.5625 Combine like terms: 42 + 217.5625 = 259.5625 217.5625 + -29.5x + x2 = 259.5625 Factor a perfect square on the left side: (x + -14.75)(x + -14.75) = 259.5625 Calculate the square root of the right side: 16.110943486 Break this problem into two subproblems by setting (x + -14.75) equal to 16.110943486 and -16.110943486.Subproblem 1
x + -14.75 = 16.110943486 Simplifying x + -14.75 = 16.110943486 Reorder the terms: -14.75 + x = 16.110943486 Solving -14.75 + x = 16.110943486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + x = 16.110943486 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + x = 16.110943486 + 14.75 x = 16.110943486 + 14.75 Combine like terms: 16.110943486 + 14.75 = 30.860943486 x = 30.860943486 Simplifying x = 30.860943486Subproblem 2
x + -14.75 = -16.110943486 Simplifying x + -14.75 = -16.110943486 Reorder the terms: -14.75 + x = -16.110943486 Solving -14.75 + x = -16.110943486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + x = -16.110943486 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + x = -16.110943486 + 14.75 x = -16.110943486 + 14.75 Combine like terms: -16.110943486 + 14.75 = -1.360943486 x = -1.360943486 Simplifying x = -1.360943486Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.860943486, -1.360943486}
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