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Simplifying 70x2 + 2x + 2 = 0 Reorder the terms: 2 + 2x + 70x2 = 0 Solving 2 + 2x + 70x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + x + 35x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + x + 35x2)' equal to zero and attempt to solve: Simplifying 1 + x + 35x2 = 0 Solving 1 + x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 0.02857142857 + 0.02857142857x + x2 = 0 Move the constant term to the right: Add '-0.02857142857' to each side of the equation. 0.02857142857 + 0.02857142857x + -0.02857142857 + x2 = 0 + -0.02857142857 Reorder the terms: 0.02857142857 + -0.02857142857 + 0.02857142857x + x2 = 0 + -0.02857142857 Combine like terms: 0.02857142857 + -0.02857142857 = 0.00000000000 0.00000000000 + 0.02857142857x + x2 = 0 + -0.02857142857 0.02857142857x + x2 = 0 + -0.02857142857 Combine like terms: 0 + -0.02857142857 = -0.02857142857 0.02857142857x + x2 = -0.02857142857 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.02857142857x + 0.25 + x2 = -0.02857142857 + 0.25 Reorder the terms: 0.25 + 0.02857142857x + x2 = -0.02857142857 + 0.25 Combine like terms: -0.02857142857 + 0.25 = 0.22142857143 0.25 + 0.02857142857x + x2 = 0.22142857143 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.22142857143 Calculate the square root of the right side: 0.470561974 Break this problem into two subproblems by setting (x + 0.5) equal to 0.470561974 and -0.470561974.Subproblem 1
x + 0.5 = 0.470561974 Simplifying x + 0.5 = 0.470561974 Reorder the terms: 0.5 + x = 0.470561974 Solving 0.5 + x = 0.470561974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.470561974 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.470561974 + -0.5 x = 0.470561974 + -0.5 Combine like terms: 0.470561974 + -0.5 = -0.029438026 x = -0.029438026 Simplifying x = -0.029438026Subproblem 2
x + 0.5 = -0.470561974 Simplifying x + 0.5 = -0.470561974 Reorder the terms: 0.5 + x = -0.470561974 Solving 0.5 + x = -0.470561974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.470561974 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.470561974 + -0.5 x = -0.470561974 + -0.5 Combine like terms: -0.470561974 + -0.5 = -0.970561974 x = -0.970561974 Simplifying x = -0.970561974Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.029438026, -0.970561974}Solution
x = {-0.029438026, -0.970561974}
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