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Simplifying 5x2 + -17x + -28 = 0 Reorder the terms: -28 + -17x + 5x2 = 0 Solving -28 + -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'. -5.6 + -3.4x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -3.4x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -3.4x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -3.4x + x2 = 0 + 5.6 -3.4x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -3.4x + x2 = 5.6 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 = 5.6 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = 5.6 + 2.89 Combine like terms: 5.6 + 2.89 = 8.49 2.89 + -3.4x + x2 = 8.49 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 8.49 Calculate the square root of the right side: 2.913760457 Break this problem into two subproblems by setting (x + -1.7) equal to 2.913760457 and -2.913760457.Subproblem 1
x + -1.7 = 2.913760457 Simplifying x + -1.7 = 2.913760457 Reorder the terms: -1.7 + x = 2.913760457 Solving -1.7 + x = 2.913760457 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 = 2.913760457 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 2.913760457 + 1.7 x = 2.913760457 + 1.7 Combine like terms: 2.913760457 + 1.7 = 4.613760457 x = 4.613760457 Simplifying x = 4.613760457Subproblem 2
x + -1.7 = -2.913760457 Simplifying x + -1.7 = -2.913760457 Reorder the terms: -1.7 + x = -2.913760457 Solving -1.7 + x = -2.913760457 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 = -2.913760457 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -2.913760457 + 1.7 x = -2.913760457 + 1.7 Combine like terms: -2.913760457 + 1.7 = -1.213760457 x = -1.213760457 Simplifying x = -1.213760457Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.613760457, -1.213760457}
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