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Simplifying (2x + 5) + -49(3.14) * x2 = 0 Reorder the terms: (5 + 2x) + -49(3.14) * x2 = 0 Remove parenthesis around (5 + 2x) 5 + 2x + -49(3.14) * x2 = 0 Multiply -49 * 3.14 5 + 2x + -153.86x2 = 0 Solving 5 + 2x + -153.86x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -153.86 the coefficient of the squared term: Divide each side by '-153.86'. -0.03249707526 + -0.01299883011x + x2 = 0 Move the constant term to the right: Add '0.03249707526' to each side of the equation. -0.03249707526 + -0.01299883011x + 0.03249707526 + x2 = 0 + 0.03249707526 Reorder the terms: -0.03249707526 + 0.03249707526 + -0.01299883011x + x2 = 0 + 0.03249707526 Combine like terms: -0.03249707526 + 0.03249707526 = 0.00000000000 0.00000000000 + -0.01299883011x + x2 = 0 + 0.03249707526 -0.01299883011x + x2 = 0 + 0.03249707526 Combine like terms: 0 + 0.03249707526 = 0.03249707526 -0.01299883011x + x2 = 0.03249707526 The x term is -0.01299883011x. Take half its coefficient (-0.006499415055). Square it (0.00004224239606) and add it to both sides. Add '0.00004224239606' to each side of the equation. -0.01299883011x + 0.00004224239606 + x2 = 0.03249707526 + 0.00004224239606 Reorder the terms: 0.00004224239606 + -0.01299883011x + x2 = 0.03249707526 + 0.00004224239606 Combine like terms: 0.03249707526 + 0.00004224239606 = 0.03253931765606 0.00004224239606 + -0.01299883011x + x2 = 0.03253931765606 Factor a perfect square on the left side: (x + -0.006499415055)(x + -0.006499415055) = 0.03253931765606 Calculate the square root of the right side: 0.180386578 Break this problem into two subproblems by setting (x + -0.006499415055) equal to 0.180386578 and -0.180386578.Subproblem 1
x + -0.006499415055 = 0.180386578 Simplifying x + -0.006499415055 = 0.180386578 Reorder the terms: -0.006499415055 + x = 0.180386578 Solving -0.006499415055 + x = 0.180386578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006499415055' to each side of the equation. -0.006499415055 + 0.006499415055 + x = 0.180386578 + 0.006499415055 Combine like terms: -0.006499415055 + 0.006499415055 = 0.000000000000 0.000000000000 + x = 0.180386578 + 0.006499415055 x = 0.180386578 + 0.006499415055 Combine like terms: 0.180386578 + 0.006499415055 = 0.186885993055 x = 0.186885993055 Simplifying x = 0.186885993055Subproblem 2
x + -0.006499415055 = -0.180386578 Simplifying x + -0.006499415055 = -0.180386578 Reorder the terms: -0.006499415055 + x = -0.180386578 Solving -0.006499415055 + x = -0.180386578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.006499415055' to each side of the equation. -0.006499415055 + 0.006499415055 + x = -0.180386578 + 0.006499415055 Combine like terms: -0.006499415055 + 0.006499415055 = 0.000000000000 0.000000000000 + x = -0.180386578 + 0.006499415055 x = -0.180386578 + 0.006499415055 Combine like terms: -0.180386578 + 0.006499415055 = -0.173887162945 x = -0.173887162945 Simplifying x = -0.173887162945Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.186885993055, -0.173887162945}
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