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Simplifying 10x2 + 12x + 3 = 0 Reorder the terms: 3 + 12x + 10x2 = 0 Solving 3 + 12x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.3 + 1.2x + x2 = 0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + 1.2x + -0.3 + x2 = 0 + -0.3 Reorder the terms: 0.3 + -0.3 + 1.2x + x2 = 0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + 1.2x + x2 = 0 + -0.3 1.2x + x2 = 0 + -0.3 Combine like terms: 0 + -0.3 = -0.3 1.2x + x2 = -0.3 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 = -0.3 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = -0.3 + 0.36 Combine like terms: -0.3 + 0.36 = 0.06 0.36 + 1.2x + x2 = 0.06 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.06 Calculate the square root of the right side: 0.244948974 Break this problem into two subproblems by setting (x + 0.6) equal to 0.244948974 and -0.244948974.Subproblem 1
x + 0.6 = 0.244948974 Simplifying x + 0.6 = 0.244948974 Reorder the terms: 0.6 + x = 0.244948974 Solving 0.6 + x = 0.244948974 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 = 0.244948974 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.244948974 + -0.6 x = 0.244948974 + -0.6 Combine like terms: 0.244948974 + -0.6 = -0.355051026 x = -0.355051026 Simplifying x = -0.355051026Subproblem 2
x + 0.6 = -0.244948974 Simplifying x + 0.6 = -0.244948974 Reorder the terms: 0.6 + x = -0.244948974 Solving 0.6 + x = -0.244948974 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 = -0.244948974 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.244948974 + -0.6 x = -0.244948974 + -0.6 Combine like terms: -0.244948974 + -0.6 = -0.844948974 x = -0.844948974 Simplifying x = -0.844948974Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.355051026, -0.844948974}
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