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Simplifying 2x(5x + -3) = 17 Reorder the terms: 2x(-3 + 5x) = 17 (-3 * 2x + 5x * 2x) = 17 (-6x + 10x2) = 17 Solving -6x + 10x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + -6x + 10x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -6x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.7 + -0.6x + x2 = 0.0 Move the constant term to the right: Add '1.7' to each side of the equation. -1.7 + -0.6x + 1.7 + x2 = 0.0 + 1.7 Reorder the terms: -1.7 + 1.7 + -0.6x + x2 = 0.0 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + -0.6x + x2 = 0.0 + 1.7 -0.6x + x2 = 0.0 + 1.7 Combine like terms: 0.0 + 1.7 = 1.7 -0.6x + x2 = 1.7 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 1.7 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 1.7 + 0.09 Combine like terms: 1.7 + 0.09 = 1.79 0.09 + -0.6x + x2 = 1.79 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 1.79 Calculate the square root of the right side: 1.337908816 Break this problem into two subproblems by setting (x + -0.3) equal to 1.337908816 and -1.337908816.Subproblem 1
x + -0.3 = 1.337908816 Simplifying x + -0.3 = 1.337908816 Reorder the terms: -0.3 + x = 1.337908816 Solving -0.3 + x = 1.337908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 1.337908816 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.337908816 + 0.3 x = 1.337908816 + 0.3 Combine like terms: 1.337908816 + 0.3 = 1.637908816 x = 1.637908816 Simplifying x = 1.637908816Subproblem 2
x + -0.3 = -1.337908816 Simplifying x + -0.3 = -1.337908816 Reorder the terms: -0.3 + x = -1.337908816 Solving -0.3 + x = -1.337908816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -1.337908816 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.337908816 + 0.3 x = -1.337908816 + 0.3 Combine like terms: -1.337908816 + 0.3 = -1.037908816 x = -1.037908816 Simplifying x = -1.037908816Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.637908816, -1.037908816}
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