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Simplifying 7x2 + 0.5x = 0.07 Reorder the terms: 0.5x + 7x2 = 0.07 Solving 0.5x + 7x2 = 0.07 Solving for variable 'x'. Reorder the terms: -0.07 + 0.5x + 7x2 = 0.07 + -0.07 Combine like terms: 0.07 + -0.07 = 0.00 -0.07 + 0.5x + 7x2 = 0.00 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.01 + 0.07142857143x + x2 = 0.00 Move the constant term to the right: Add '0.01' to each side of the equation. -0.01 + 0.07142857143x + 0.01 + x2 = 0.00 + 0.01 Reorder the terms: -0.01 + 0.01 + 0.07142857143x + x2 = 0.00 + 0.01 Combine like terms: -0.01 + 0.01 = 0.00 0.00 + 0.07142857143x + x2 = 0.00 + 0.01 0.07142857143x + x2 = 0.00 + 0.01 Combine like terms: 0.00 + 0.01 = 0.01 0.07142857143x + x2 = 0.01 The x term is 0.07142857143x. Take half its coefficient (0.03571428572). Square it (0.001275510204) and add it to both sides. Add '0.001275510204' to each side of the equation. 0.07142857143x + 0.001275510204 + x2 = 0.01 + 0.001275510204 Reorder the terms: 0.001275510204 + 0.07142857143x + x2 = 0.01 + 0.001275510204 Combine like terms: 0.01 + 0.001275510204 = 0.011275510204 0.001275510204 + 0.07142857143x + x2 = 0.011275510204 Factor a perfect square on the left side: (x + 0.03571428572)(x + 0.03571428572) = 0.011275510204 Calculate the square root of the right side: 0.106186205 Break this problem into two subproblems by setting (x + 0.03571428572) equal to 0.106186205 and -0.106186205.Subproblem 1
x + 0.03571428572 = 0.106186205 Simplifying x + 0.03571428572 = 0.106186205 Reorder the terms: 0.03571428572 + x = 0.106186205 Solving 0.03571428572 + x = 0.106186205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03571428572' to each side of the equation. 0.03571428572 + -0.03571428572 + x = 0.106186205 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = 0.106186205 + -0.03571428572 x = 0.106186205 + -0.03571428572 Combine like terms: 0.106186205 + -0.03571428572 = 0.07047191928 x = 0.07047191928 Simplifying x = 0.07047191928Subproblem 2
x + 0.03571428572 = -0.106186205 Simplifying x + 0.03571428572 = -0.106186205 Reorder the terms: 0.03571428572 + x = -0.106186205 Solving 0.03571428572 + x = -0.106186205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03571428572' to each side of the equation. 0.03571428572 + -0.03571428572 + x = -0.106186205 + -0.03571428572 Combine like terms: 0.03571428572 + -0.03571428572 = 0.00000000000 0.00000000000 + x = -0.106186205 + -0.03571428572 x = -0.106186205 + -0.03571428572 Combine like terms: -0.106186205 + -0.03571428572 = -0.14190049072 x = -0.14190049072 Simplifying x = -0.14190049072Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.07047191928, -0.14190049072}
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