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Simplifying 3 + -1x(20x + 12) = 0 Reorder the terms: 3 + -1x(12 + 20x) = 0 3 + (12 * -1x + 20x * -1x) = 0 3 + (-12x + -20x2) = 0 Solving 3 + -12x + -20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -0.15 + 0.6x + x2 = 0.0 Move the constant term to the right: Add '0.15' to each side of the equation. -0.15 + 0.6x + 0.15 + x2 = 0.0 + 0.15 Reorder the terms: -0.15 + 0.15 + 0.6x + x2 = 0.0 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + 0.6x + x2 = 0.0 + 0.15 0.6x + x2 = 0.0 + 0.15 Combine like terms: 0.0 + 0.15 = 0.15 0.6x + x2 = 0.15 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 0.15 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 0.15 + 0.09 Combine like terms: 0.15 + 0.09 = 0.24 0.09 + 0.6x + x2 = 0.24 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x + 0.3) equal to 0.489897949 and -0.489897949.Subproblem 1
x + 0.3 = 0.489897949 Simplifying x + 0.3 = 0.489897949 Reorder the terms: 0.3 + x = 0.489897949 Solving 0.3 + x = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 0.489897949 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.489897949 + -0.3 x = 0.489897949 + -0.3 Combine like terms: 0.489897949 + -0.3 = 0.189897949 x = 0.189897949 Simplifying x = 0.189897949Subproblem 2
x + 0.3 = -0.489897949 Simplifying x + 0.3 = -0.489897949 Reorder the terms: 0.3 + x = -0.489897949 Solving 0.3 + x = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -0.489897949 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.489897949 + -0.3 x = -0.489897949 + -0.3 Combine like terms: -0.489897949 + -0.3 = -0.789897949 x = -0.789897949 Simplifying x = -0.789897949Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.189897949, -0.789897949}
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