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Simplifying -5x2 + 17x + -10 = 0 Reorder the terms: -10 + 17x + -5x2 = 0 Solving -10 + 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'. 2 + -3.4x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.4x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -3.4x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.4x + x2 = 0 + -2 -3.4x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.4x + x2 = -2 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 = -2 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = -2 + 2.89 Combine like terms: -2 + 2.89 = 0.89 2.89 + -3.4x + x2 = 0.89 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (x + -1.7) equal to 0.943398113 and -0.943398113.Subproblem 1
x + -1.7 = 0.943398113 Simplifying x + -1.7 = 0.943398113 Reorder the terms: -1.7 + x = 0.943398113 Solving -1.7 + x = 0.943398113 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 = 0.943398113 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 0.943398113 + 1.7 x = 0.943398113 + 1.7 Combine like terms: 0.943398113 + 1.7 = 2.643398113 x = 2.643398113 Simplifying x = 2.643398113Subproblem 2
x + -1.7 = -0.943398113 Simplifying x + -1.7 = -0.943398113 Reorder the terms: -1.7 + x = -0.943398113 Solving -1.7 + x = -0.943398113 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 = -0.943398113 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -0.943398113 + 1.7 x = -0.943398113 + 1.7 Combine like terms: -0.943398113 + 1.7 = 0.756601887 x = 0.756601887 Simplifying x = 0.756601887Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.643398113, 0.756601887}
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