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Simplifying 10x2 + -30x + 17 = 0 Reorder the terms: 17 + -30x + 10x2 = 0 Solving 17 + -30x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.7 + -3x + x2 = 0 Move the constant term to the right: Add '-1.7' to each side of the equation. 1.7 + -3x + -1.7 + x2 = 0 + -1.7 Reorder the terms: 1.7 + -1.7 + -3x + x2 = 0 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + -3x + x2 = 0 + -1.7 -3x + x2 = 0 + -1.7 Combine like terms: 0 + -1.7 = -1.7 -3x + x2 = -1.7 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.7 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.7 + 2.25 Combine like terms: -1.7 + 2.25 = 0.55 2.25 + -3x + x2 = 0.55 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.55 Calculate the square root of the right side: 0.741619849 Break this problem into two subproblems by setting (x + -1.5) equal to 0.741619849 and -0.741619849.Subproblem 1
x + -1.5 = 0.741619849 Simplifying x + -1.5 = 0.741619849 Reorder the terms: -1.5 + x = 0.741619849 Solving -1.5 + x = 0.741619849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.741619849 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.741619849 + 1.5 x = 0.741619849 + 1.5 Combine like terms: 0.741619849 + 1.5 = 2.241619849 x = 2.241619849 Simplifying x = 2.241619849Subproblem 2
x + -1.5 = -0.741619849 Simplifying x + -1.5 = -0.741619849 Reorder the terms: -1.5 + x = -0.741619849 Solving -1.5 + x = -0.741619849 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.741619849 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.741619849 + 1.5 x = -0.741619849 + 1.5 Combine like terms: -0.741619849 + 1.5 = 0.758380151 x = 0.758380151 Simplifying x = 0.758380151Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.241619849, 0.758380151}
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