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Simplifying 2x2 + -15x + -84 = 0 Reorder the terms: -84 + -15x + 2x2 = 0 Solving -84 + -15x + 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 + -7.5x + x2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + -7.5x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -7.5x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -7.5x + x2 = 0 + 42 -7.5x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -7.5x + x2 = 42 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 42 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 42 + 14.0625 Combine like terms: 42 + 14.0625 = 56.0625 14.0625 + -7.5x + x2 = 56.0625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 56.0625 Calculate the square root of the right side: 7.487489566 Break this problem into two subproblems by setting (x + -3.75) equal to 7.487489566 and -7.487489566.Subproblem 1
x + -3.75 = 7.487489566 Simplifying x + -3.75 = 7.487489566 Reorder the terms: -3.75 + x = 7.487489566 Solving -3.75 + x = 7.487489566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 7.487489566 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 7.487489566 + 3.75 x = 7.487489566 + 3.75 Combine like terms: 7.487489566 + 3.75 = 11.237489566 x = 11.237489566 Simplifying x = 11.237489566Subproblem 2
x + -3.75 = -7.487489566 Simplifying x + -3.75 = -7.487489566 Reorder the terms: -3.75 + x = -7.487489566 Solving -3.75 + x = -7.487489566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -7.487489566 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -7.487489566 + 3.75 x = -7.487489566 + 3.75 Combine like terms: -7.487489566 + 3.75 = -3.737489566 x = -3.737489566 Simplifying x = -3.737489566Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.237489566, -3.737489566}
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