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Simplifying 29x2 + -6x + -42 = 0 Reorder the terms: -42 + -6x + 29x2 = 0 Solving -42 + -6x + 29x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. -1.448275862 + -0.2068965517x + x2 = 0 Move the constant term to the right: Add '1.448275862' to each side of the equation. -1.448275862 + -0.2068965517x + 1.448275862 + x2 = 0 + 1.448275862 Reorder the terms: -1.448275862 + 1.448275862 + -0.2068965517x + x2 = 0 + 1.448275862 Combine like terms: -1.448275862 + 1.448275862 = 0.000000000 0.000000000 + -0.2068965517x + x2 = 0 + 1.448275862 -0.2068965517x + x2 = 0 + 1.448275862 Combine like terms: 0 + 1.448275862 = 1.448275862 -0.2068965517x + x2 = 1.448275862 The x term is -0.2068965517x. Take half its coefficient (-0.1034482759). Square it (0.01070154579) and add it to both sides. Add '0.01070154579' to each side of the equation. -0.2068965517x + 0.01070154579 + x2 = 1.448275862 + 0.01070154579 Reorder the terms: 0.01070154579 + -0.2068965517x + x2 = 1.448275862 + 0.01070154579 Combine like terms: 1.448275862 + 0.01070154579 = 1.45897740779 0.01070154579 + -0.2068965517x + x2 = 1.45897740779 Factor a perfect square on the left side: (x + -0.1034482759)(x + -0.1034482759) = 1.45897740779 Calculate the square root of the right side: 1.207881372 Break this problem into two subproblems by setting (x + -0.1034482759) equal to 1.207881372 and -1.207881372.Subproblem 1
x + -0.1034482759 = 1.207881372 Simplifying x + -0.1034482759 = 1.207881372 Reorder the terms: -0.1034482759 + x = 1.207881372 Solving -0.1034482759 + x = 1.207881372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1034482759' to each side of the equation. -0.1034482759 + 0.1034482759 + x = 1.207881372 + 0.1034482759 Combine like terms: -0.1034482759 + 0.1034482759 = 0.0000000000 0.0000000000 + x = 1.207881372 + 0.1034482759 x = 1.207881372 + 0.1034482759 Combine like terms: 1.207881372 + 0.1034482759 = 1.3113296479 x = 1.3113296479 Simplifying x = 1.3113296479Subproblem 2
x + -0.1034482759 = -1.207881372 Simplifying x + -0.1034482759 = -1.207881372 Reorder the terms: -0.1034482759 + x = -1.207881372 Solving -0.1034482759 + x = -1.207881372 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1034482759' to each side of the equation. -0.1034482759 + 0.1034482759 + x = -1.207881372 + 0.1034482759 Combine like terms: -0.1034482759 + 0.1034482759 = 0.0000000000 0.0000000000 + x = -1.207881372 + 0.1034482759 x = -1.207881372 + 0.1034482759 Combine like terms: -1.207881372 + 0.1034482759 = -1.1044330961 x = -1.1044330961 Simplifying x = -1.1044330961Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3113296479, -1.1044330961}
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