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Simplifying 2x2 + -30x + -17 = 0 Reorder the terms: -17 + -30x + 2x2 = 0 Solving -17 + -30x + 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'. -8.5 + -15x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -15x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -15x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -15x + x2 = 0 + 8.5 -15x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -15x + x2 = 8.5 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 8.5 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 8.5 + 56.25 Combine like terms: 8.5 + 56.25 = 64.75 56.25 + -15x + x2 = 64.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 64.75 Calculate the square root of the right side: 8.04673847 Break this problem into two subproblems by setting (x + -7.5) equal to 8.04673847 and -8.04673847.Subproblem 1
x + -7.5 = 8.04673847 Simplifying x + -7.5 = 8.04673847 Reorder the terms: -7.5 + x = 8.04673847 Solving -7.5 + x = 8.04673847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 8.04673847 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 8.04673847 + 7.5 x = 8.04673847 + 7.5 Combine like terms: 8.04673847 + 7.5 = 15.54673847 x = 15.54673847 Simplifying x = 15.54673847Subproblem 2
x + -7.5 = -8.04673847 Simplifying x + -7.5 = -8.04673847 Reorder the terms: -7.5 + x = -8.04673847 Solving -7.5 + x = -8.04673847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -8.04673847 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -8.04673847 + 7.5 x = -8.04673847 + 7.5 Combine like terms: -8.04673847 + 7.5 = -0.54673847 x = -0.54673847 Simplifying x = -0.54673847Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.54673847, -0.54673847}
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