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Simplifying 60x2 + 25x + -9 = 0 Reorder the terms: -9 + 25x + 60x2 = 0 Solving -9 + 25x + 60x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 60 the coefficient of the squared term: Divide each side by '60'. -0.15 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '0.15' to each side of the equation. -0.15 + 0.4166666667x + 0.15 + x2 = 0 + 0.15 Reorder the terms: -0.15 + 0.15 + 0.4166666667x + x2 = 0 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + 0.4166666667x + x2 = 0 + 0.15 0.4166666667x + x2 = 0 + 0.15 Combine like terms: 0 + 0.15 = 0.15 0.4166666667x + x2 = 0.15 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = 0.15 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 0.15 + 0.04340277781 Combine like terms: 0.15 + 0.04340277781 = 0.19340277781 0.04340277781 + 0.4166666667x + x2 = 0.19340277781 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 0.19340277781 Calculate the square root of the right side: 0.439775827 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 0.439775827 and -0.439775827.Subproblem 1
x + 0.2083333334 = 0.439775827 Simplifying x + 0.2083333334 = 0.439775827 Reorder the terms: 0.2083333334 + x = 0.439775827 Solving 0.2083333334 + x = 0.439775827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 0.439775827 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 0.439775827 + -0.2083333334 x = 0.439775827 + -0.2083333334 Combine like terms: 0.439775827 + -0.2083333334 = 0.2314424936 x = 0.2314424936 Simplifying x = 0.2314424936Subproblem 2
x + 0.2083333334 = -0.439775827 Simplifying x + 0.2083333334 = -0.439775827 Reorder the terms: 0.2083333334 + x = -0.439775827 Solving 0.2083333334 + x = -0.439775827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -0.439775827 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -0.439775827 + -0.2083333334 x = -0.439775827 + -0.2083333334 Combine like terms: -0.439775827 + -0.2083333334 = -0.6481091604 x = -0.6481091604 Simplifying x = -0.6481091604Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2314424936, -0.6481091604}
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