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Simplifying 15x2 + -84x + 5 = 0 Reorder the terms: 5 + -84x + 15x2 = 0 Solving 5 + -84x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 0.3333333333 + -5.6x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -5.6x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -5.6x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -5.6x + x2 = 0 + -0.3333333333 -5.6x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -5.6x + x2 = -0.3333333333 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = -0.3333333333 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = -0.3333333333 + 7.84 Combine like terms: -0.3333333333 + 7.84 = 7.5066666667 7.84 + -5.6x + x2 = 7.5066666667 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 7.5066666667 Calculate the square root of the right side: 2.739829678 Break this problem into two subproblems by setting (x + -2.8) equal to 2.739829678 and -2.739829678.Subproblem 1
x + -2.8 = 2.739829678 Simplifying x + -2.8 = 2.739829678 Reorder the terms: -2.8 + x = 2.739829678 Solving -2.8 + x = 2.739829678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 2.739829678 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 2.739829678 + 2.8 x = 2.739829678 + 2.8 Combine like terms: 2.739829678 + 2.8 = 5.539829678 x = 5.539829678 Simplifying x = 5.539829678Subproblem 2
x + -2.8 = -2.739829678 Simplifying x + -2.8 = -2.739829678 Reorder the terms: -2.8 + x = -2.739829678 Solving -2.8 + x = -2.739829678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -2.739829678 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -2.739829678 + 2.8 x = -2.739829678 + 2.8 Combine like terms: -2.739829678 + 2.8 = 0.060170322 x = 0.060170322 Simplifying x = 0.060170322Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.539829678, 0.060170322}
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