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Simplifying 70x2 + 2x + -7 = 0 Reorder the terms: -7 + 2x + 70x2 = 0 Solving -7 + 2x + 70x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 70 the coefficient of the squared term: Divide each side by '70'. -0.1 + 0.02857142857x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.02857142857x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.02857142857x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.02857142857x + x2 = 0 + 0.1 0.02857142857x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 0.02857142857x + x2 = 0.1 The x term is 0.02857142857x. Take half its coefficient (0.01428571429). Square it (0.0002040816328) and add it to both sides. Add '0.0002040816328' to each side of the equation. 0.02857142857x + 0.0002040816328 + x2 = 0.1 + 0.0002040816328 Reorder the terms: 0.0002040816328 + 0.02857142857x + x2 = 0.1 + 0.0002040816328 Combine like terms: 0.1 + 0.0002040816328 = 0.1002040816328 0.0002040816328 + 0.02857142857x + x2 = 0.1002040816328 Factor a perfect square on the left side: (x + 0.01428571429)(x + 0.01428571429) = 0.1002040816328 Calculate the square root of the right side: 0.316550283 Break this problem into two subproblems by setting (x + 0.01428571429) equal to 0.316550283 and -0.316550283.Subproblem 1
x + 0.01428571429 = 0.316550283 Simplifying x + 0.01428571429 = 0.316550283 Reorder the terms: 0.01428571429 + x = 0.316550283 Solving 0.01428571429 + x = 0.316550283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01428571429' to each side of the equation. 0.01428571429 + -0.01428571429 + x = 0.316550283 + -0.01428571429 Combine like terms: 0.01428571429 + -0.01428571429 = 0.00000000000 0.00000000000 + x = 0.316550283 + -0.01428571429 x = 0.316550283 + -0.01428571429 Combine like terms: 0.316550283 + -0.01428571429 = 0.30226456871 x = 0.30226456871 Simplifying x = 0.30226456871Subproblem 2
x + 0.01428571429 = -0.316550283 Simplifying x + 0.01428571429 = -0.316550283 Reorder the terms: 0.01428571429 + x = -0.316550283 Solving 0.01428571429 + x = -0.316550283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01428571429' to each side of the equation. 0.01428571429 + -0.01428571429 + x = -0.316550283 + -0.01428571429 Combine like terms: 0.01428571429 + -0.01428571429 = 0.00000000000 0.00000000000 + x = -0.316550283 + -0.01428571429 x = -0.316550283 + -0.01428571429 Combine like terms: -0.316550283 + -0.01428571429 = -0.33083599729 x = -0.33083599729 Simplifying x = -0.33083599729Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.30226456871, -0.33083599729}
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