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Simplifying 5x2 + -17x + -30 = 0 Reorder the terms: -30 + -17x + 5x2 = 0 Solving -30 + -17x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6 + -3.4x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -3.4x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -3.4x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -3.4x + x2 = 0 + 6 -3.4x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -3.4x + x2 = 6 The x term is -3.4x. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4x + 2.89 + x2 = 6 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 6 + 2.89 Combine like terms: 6 + 2.89 = 8.89 2.89 + -3.4x + x2 = 8.89 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 8.89 Calculate the square root of the right side: 2.981610303 Break this problem into two subproblems by setting (x + -1.7) equal to 2.981610303 and -2.981610303.Subproblem 1
x + -1.7 = 2.981610303 Simplifying x + -1.7 = 2.981610303 Reorder the terms: -1.7 + x = 2.981610303 Solving -1.7 + x = 2.981610303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = 2.981610303 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 2.981610303 + 1.7 x = 2.981610303 + 1.7 Combine like terms: 2.981610303 + 1.7 = 4.681610303 x = 4.681610303 Simplifying x = 4.681610303Subproblem 2
x + -1.7 = -2.981610303 Simplifying x + -1.7 = -2.981610303 Reorder the terms: -1.7 + x = -2.981610303 Solving -1.7 + x = -2.981610303 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + x = -2.981610303 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -2.981610303 + 1.7 x = -2.981610303 + 1.7 Combine like terms: -2.981610303 + 1.7 = -1.281610303 x = -1.281610303 Simplifying x = -1.281610303Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.681610303, -1.281610303}
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