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Simplifying 25x2 + 60x + 9 = 0 Reorder the terms: 9 + 60x + 25x2 = 0 Solving 9 + 60x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.36 + 2.4x + x2 = 0 Move the constant term to the right: Add '-0.36' to each side of the equation. 0.36 + 2.4x + -0.36 + x2 = 0 + -0.36 Reorder the terms: 0.36 + -0.36 + 2.4x + x2 = 0 + -0.36 Combine like terms: 0.36 + -0.36 = 0.00 0.00 + 2.4x + x2 = 0 + -0.36 2.4x + x2 = 0 + -0.36 Combine like terms: 0 + -0.36 = -0.36 2.4x + x2 = -0.36 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = -0.36 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = -0.36 + 1.44 Combine like terms: -0.36 + 1.44 = 1.08 1.44 + 2.4x + x2 = 1.08 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 1.08 Calculate the square root of the right side: 1.039230485 Break this problem into two subproblems by setting (x + 1.2) equal to 1.039230485 and -1.039230485.Subproblem 1
x + 1.2 = 1.039230485 Simplifying x + 1.2 = 1.039230485 Reorder the terms: 1.2 + x = 1.039230485 Solving 1.2 + x = 1.039230485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 1.039230485 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.039230485 + -1.2 x = 1.039230485 + -1.2 Combine like terms: 1.039230485 + -1.2 = -0.160769515 x = -0.160769515 Simplifying x = -0.160769515Subproblem 2
x + 1.2 = -1.039230485 Simplifying x + 1.2 = -1.039230485 Reorder the terms: 1.2 + x = -1.039230485 Solving 1.2 + x = -1.039230485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -1.039230485 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.039230485 + -1.2 x = -1.039230485 + -1.2 Combine like terms: -1.039230485 + -1.2 = -2.239230485 x = -2.239230485 Simplifying x = -2.239230485Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.160769515, -2.239230485}
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