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Simplifying 42x2 + 16x + -93 = 0 Reorder the terms: -93 + 16x + 42x2 = 0 Solving -93 + 16x + 42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -2.214285714 + 0.380952381x + x2 = 0 Move the constant term to the right: Add '2.214285714' to each side of the equation. -2.214285714 + 0.380952381x + 2.214285714 + x2 = 0 + 2.214285714 Reorder the terms: -2.214285714 + 2.214285714 + 0.380952381x + x2 = 0 + 2.214285714 Combine like terms: -2.214285714 + 2.214285714 = 0.000000000 0.000000000 + 0.380952381x + x2 = 0 + 2.214285714 0.380952381x + x2 = 0 + 2.214285714 Combine like terms: 0 + 2.214285714 = 2.214285714 0.380952381x + x2 = 2.214285714 The x term is 0.380952381x. Take half its coefficient (0.1904761905). Square it (0.03628117915) and add it to both sides. Add '0.03628117915' to each side of the equation. 0.380952381x + 0.03628117915 + x2 = 2.214285714 + 0.03628117915 Reorder the terms: 0.03628117915 + 0.380952381x + x2 = 2.214285714 + 0.03628117915 Combine like terms: 2.214285714 + 0.03628117915 = 2.25056689315 0.03628117915 + 0.380952381x + x2 = 2.25056689315 Factor a perfect square on the left side: (x + 0.1904761905)(x + 0.1904761905) = 2.25056689315 Calculate the square root of the right side: 1.500188952 Break this problem into two subproblems by setting (x + 0.1904761905) equal to 1.500188952 and -1.500188952.Subproblem 1
x + 0.1904761905 = 1.500188952 Simplifying x + 0.1904761905 = 1.500188952 Reorder the terms: 0.1904761905 + x = 1.500188952 Solving 0.1904761905 + x = 1.500188952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1904761905' to each side of the equation. 0.1904761905 + -0.1904761905 + x = 1.500188952 + -0.1904761905 Combine like terms: 0.1904761905 + -0.1904761905 = 0.0000000000 0.0000000000 + x = 1.500188952 + -0.1904761905 x = 1.500188952 + -0.1904761905 Combine like terms: 1.500188952 + -0.1904761905 = 1.3097127615 x = 1.3097127615 Simplifying x = 1.3097127615Subproblem 2
x + 0.1904761905 = -1.500188952 Simplifying x + 0.1904761905 = -1.500188952 Reorder the terms: 0.1904761905 + x = -1.500188952 Solving 0.1904761905 + x = -1.500188952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1904761905' to each side of the equation. 0.1904761905 + -0.1904761905 + x = -1.500188952 + -0.1904761905 Combine like terms: 0.1904761905 + -0.1904761905 = 0.0000000000 0.0000000000 + x = -1.500188952 + -0.1904761905 x = -1.500188952 + -0.1904761905 Combine like terms: -1.500188952 + -0.1904761905 = -1.6906651425 x = -1.6906651425 Simplifying x = -1.6906651425Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3097127615, -1.6906651425}
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