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Simplifying 15x2 + -51x + 15 = 0 Reorder the terms: 15 + -51x + 15x2 = 0 Solving 15 + -51x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -17x + 5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -17x + 5x2)' equal to zero and attempt to solve: Simplifying 5 + -17x + 5x2 = 0 Solving 5 + -17x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + -3.4x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -3.4x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -3.4x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3.4x + x2 = 0 + -1 -3.4x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3.4x + x2 = -1 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 = -1 + 2.89 Reorder the terms: 2.89 + -3.4x + x2 = -1 + 2.89 Combine like terms: -1 + 2.89 = 1.89 2.89 + -3.4x + x2 = 1.89 Factor a perfect square on the left side: (x + -1.7)(x + -1.7) = 1.89 Calculate the square root of the right side: 1.374772708 Break this problem into two subproblems by setting (x + -1.7) equal to 1.374772708 and -1.374772708.Subproblem 1
x + -1.7 = 1.374772708 Simplifying x + -1.7 = 1.374772708 Reorder the terms: -1.7 + x = 1.374772708 Solving -1.7 + x = 1.374772708 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 = 1.374772708 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = 1.374772708 + 1.7 x = 1.374772708 + 1.7 Combine like terms: 1.374772708 + 1.7 = 3.074772708 x = 3.074772708 Simplifying x = 3.074772708Subproblem 2
x + -1.7 = -1.374772708 Simplifying x + -1.7 = -1.374772708 Reorder the terms: -1.7 + x = -1.374772708 Solving -1.7 + x = -1.374772708 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 = -1.374772708 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + x = -1.374772708 + 1.7 x = -1.374772708 + 1.7 Combine like terms: -1.374772708 + 1.7 = 0.325227292 x = 0.325227292 Simplifying x = 0.325227292Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.074772708, 0.325227292}Solution
x = {3.074772708, 0.325227292}
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