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Simplifying 10x2 + -70x + 4 = 0 Reorder the terms: 4 + -70x + 10x2 = 0 Solving 4 + -70x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -35x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -35x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + -35x + 5x2 = 0 Solving 2 + -35x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -7x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -7x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -7x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -7x + x2 = 0 + -0.4 -7x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -7x + x2 = -0.4 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -0.4 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -0.4 + 12.25 Combine like terms: -0.4 + 12.25 = 11.85 12.25 + -7x + x2 = 11.85 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 11.85 Calculate the square root of the right side: 3.442382896 Break this problem into two subproblems by setting (x + -3.5) equal to 3.442382896 and -3.442382896.Subproblem 1
x + -3.5 = 3.442382896 Simplifying x + -3.5 = 3.442382896 Reorder the terms: -3.5 + x = 3.442382896 Solving -3.5 + x = 3.442382896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.442382896 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.442382896 + 3.5 x = 3.442382896 + 3.5 Combine like terms: 3.442382896 + 3.5 = 6.942382896 x = 6.942382896 Simplifying x = 6.942382896Subproblem 2
x + -3.5 = -3.442382896 Simplifying x + -3.5 = -3.442382896 Reorder the terms: -3.5 + x = -3.442382896 Solving -3.5 + x = -3.442382896 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.442382896 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.442382896 + 3.5 x = -3.442382896 + 3.5 Combine like terms: -3.442382896 + 3.5 = 0.057617104 x = 0.057617104 Simplifying x = 0.057617104Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.942382896, 0.057617104}Solution
x = {6.942382896, 0.057617104}
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