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Simplifying 17x2 + -16x + -12 = 0 Reorder the terms: -12 + -16x + 17x2 = 0 Solving -12 + -16x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.7058823529 + -0.9411764706x + x2 = 0 Move the constant term to the right: Add '0.7058823529' to each side of the equation. -0.7058823529 + -0.9411764706x + 0.7058823529 + x2 = 0 + 0.7058823529 Reorder the terms: -0.7058823529 + 0.7058823529 + -0.9411764706x + x2 = 0 + 0.7058823529 Combine like terms: -0.7058823529 + 0.7058823529 = 0.0000000000 0.0000000000 + -0.9411764706x + x2 = 0 + 0.7058823529 -0.9411764706x + x2 = 0 + 0.7058823529 Combine like terms: 0 + 0.7058823529 = 0.7058823529 -0.9411764706x + x2 = 0.7058823529 The x term is -0.9411764706x. Take half its coefficient (-0.4705882353). Square it (0.2214532872) and add it to both sides. Add '0.2214532872' to each side of the equation. -0.9411764706x + 0.2214532872 + x2 = 0.7058823529 + 0.2214532872 Reorder the terms: 0.2214532872 + -0.9411764706x + x2 = 0.7058823529 + 0.2214532872 Combine like terms: 0.7058823529 + 0.2214532872 = 0.9273356401 0.2214532872 + -0.9411764706x + x2 = 0.9273356401 Factor a perfect square on the left side: (x + -0.4705882353)(x + -0.4705882353) = 0.9273356401 Calculate the square root of the right side: 0.962982679 Break this problem into two subproblems by setting (x + -0.4705882353) equal to 0.962982679 and -0.962982679.Subproblem 1
x + -0.4705882353 = 0.962982679 Simplifying x + -0.4705882353 = 0.962982679 Reorder the terms: -0.4705882353 + x = 0.962982679 Solving -0.4705882353 + x = 0.962982679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4705882353' to each side of the equation. -0.4705882353 + 0.4705882353 + x = 0.962982679 + 0.4705882353 Combine like terms: -0.4705882353 + 0.4705882353 = 0.0000000000 0.0000000000 + x = 0.962982679 + 0.4705882353 x = 0.962982679 + 0.4705882353 Combine like terms: 0.962982679 + 0.4705882353 = 1.4335709143 x = 1.4335709143 Simplifying x = 1.4335709143Subproblem 2
x + -0.4705882353 = -0.962982679 Simplifying x + -0.4705882353 = -0.962982679 Reorder the terms: -0.4705882353 + x = -0.962982679 Solving -0.4705882353 + x = -0.962982679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4705882353' to each side of the equation. -0.4705882353 + 0.4705882353 + x = -0.962982679 + 0.4705882353 Combine like terms: -0.4705882353 + 0.4705882353 = 0.0000000000 0.0000000000 + x = -0.962982679 + 0.4705882353 x = -0.962982679 + 0.4705882353 Combine like terms: -0.962982679 + 0.4705882353 = -0.4923944437 x = -0.4923944437 Simplifying x = -0.4923944437Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4335709143, -0.4923944437}
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