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Simplifying 49x2 + 5x = 1500 Reorder the terms: 5x + 49x2 = 1500 Solving 5x + 49x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + 5x + 49x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + 5x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -30.6122449 + 0.1020408163x + x2 = 0 Move the constant term to the right: Add '30.6122449' to each side of the equation. -30.6122449 + 0.1020408163x + 30.6122449 + x2 = 0 + 30.6122449 Reorder the terms: -30.6122449 + 30.6122449 + 0.1020408163x + x2 = 0 + 30.6122449 Combine like terms: -30.6122449 + 30.6122449 = 0.0000000 0.0000000 + 0.1020408163x + x2 = 0 + 30.6122449 0.1020408163x + x2 = 0 + 30.6122449 Combine like terms: 0 + 30.6122449 = 30.6122449 0.1020408163x + x2 = 30.6122449 The x term is 0.1020408163x. Take half its coefficient (0.05102040815). Square it (0.002603082048) and add it to both sides. Add '0.002603082048' to each side of the equation. 0.1020408163x + 0.002603082048 + x2 = 30.6122449 + 0.002603082048 Reorder the terms: 0.002603082048 + 0.1020408163x + x2 = 30.6122449 + 0.002603082048 Combine like terms: 30.6122449 + 0.002603082048 = 30.614847982048 0.002603082048 + 0.1020408163x + x2 = 30.614847982048 Factor a perfect square on the left side: (x + 0.05102040815)(x + 0.05102040815) = 30.614847982048 Calculate the square root of the right side: 5.533068586 Break this problem into two subproblems by setting (x + 0.05102040815) equal to 5.533068586 and -5.533068586.Subproblem 1
x + 0.05102040815 = 5.533068586 Simplifying x + 0.05102040815 = 5.533068586 Reorder the terms: 0.05102040815 + x = 5.533068586 Solving 0.05102040815 + x = 5.533068586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05102040815' to each side of the equation. 0.05102040815 + -0.05102040815 + x = 5.533068586 + -0.05102040815 Combine like terms: 0.05102040815 + -0.05102040815 = 0.00000000000 0.00000000000 + x = 5.533068586 + -0.05102040815 x = 5.533068586 + -0.05102040815 Combine like terms: 5.533068586 + -0.05102040815 = 5.48204817785 x = 5.48204817785 Simplifying x = 5.48204817785Subproblem 2
x + 0.05102040815 = -5.533068586 Simplifying x + 0.05102040815 = -5.533068586 Reorder the terms: 0.05102040815 + x = -5.533068586 Solving 0.05102040815 + x = -5.533068586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05102040815' to each side of the equation. 0.05102040815 + -0.05102040815 + x = -5.533068586 + -0.05102040815 Combine like terms: 0.05102040815 + -0.05102040815 = 0.00000000000 0.00000000000 + x = -5.533068586 + -0.05102040815 x = -5.533068586 + -0.05102040815 Combine like terms: -5.533068586 + -0.05102040815 = -5.58408899415 x = -5.58408899415 Simplifying x = -5.58408899415Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.48204817785, -5.58408899415}
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