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Simplifying 25x2 + -30x = 166 Reorder the terms: -30x + 25x2 = 166 Solving -30x + 25x2 = 166 Solving for variable 'x'. Reorder the terms: -166 + -30x + 25x2 = 166 + -166 Combine like terms: 166 + -166 = 0 -166 + -30x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -6.64 + -1.2x + x2 = 0 Move the constant term to the right: Add '6.64' to each side of the equation. -6.64 + -1.2x + 6.64 + x2 = 0 + 6.64 Reorder the terms: -6.64 + 6.64 + -1.2x + x2 = 0 + 6.64 Combine like terms: -6.64 + 6.64 = 0.00 0.00 + -1.2x + x2 = 0 + 6.64 -1.2x + x2 = 0 + 6.64 Combine like terms: 0 + 6.64 = 6.64 -1.2x + x2 = 6.64 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 6.64 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 6.64 + 0.36 Combine like terms: 6.64 + 0.36 = 7 0.36 + -1.2x + x2 = 7 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -0.6) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -0.6 = 2.645751311 Simplifying x + -0.6 = 2.645751311 Reorder the terms: -0.6 + x = 2.645751311 Solving -0.6 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 2.645751311 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 2.645751311 + 0.6 x = 2.645751311 + 0.6 Combine like terms: 2.645751311 + 0.6 = 3.245751311 x = 3.245751311 Simplifying x = 3.245751311Subproblem 2
x + -0.6 = -2.645751311 Simplifying x + -0.6 = -2.645751311 Reorder the terms: -0.6 + x = -2.645751311 Solving -0.6 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -2.645751311 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -2.645751311 + 0.6 x = -2.645751311 + 0.6 Combine like terms: -2.645751311 + 0.6 = -2.045751311 x = -2.045751311 Simplifying x = -2.045751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.245751311, -2.045751311}
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