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Simplifying 0.6303 + -7.145x + 10.5x2 = 0 Solving 0.6303 + -7.145x + 10.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10.5 the coefficient of the squared term: Divide each side by '10.5'. 0.06002857143 + -0.6804761905x + x2 = 0 Move the constant term to the right: Add '-0.06002857143' to each side of the equation. 0.06002857143 + -0.6804761905x + -0.06002857143 + x2 = 0 + -0.06002857143 Reorder the terms: 0.06002857143 + -0.06002857143 + -0.6804761905x + x2 = 0 + -0.06002857143 Combine like terms: 0.06002857143 + -0.06002857143 = 0.00000000000 0.00000000000 + -0.6804761905x + x2 = 0 + -0.06002857143 -0.6804761905x + x2 = 0 + -0.06002857143 Combine like terms: 0 + -0.06002857143 = -0.06002857143 -0.6804761905x + x2 = -0.06002857143 The x term is -0.6804761905x. Take half its coefficient (-0.3402380953). Square it (0.1157619615) and add it to both sides. Add '0.1157619615' to each side of the equation. -0.6804761905x + 0.1157619615 + x2 = -0.06002857143 + 0.1157619615 Reorder the terms: 0.1157619615 + -0.6804761905x + x2 = -0.06002857143 + 0.1157619615 Combine like terms: -0.06002857143 + 0.1157619615 = 0.05573339007 0.1157619615 + -0.6804761905x + x2 = 0.05573339007 Factor a perfect square on the left side: (x + -0.3402380953)(x + -0.3402380953) = 0.05573339007 Calculate the square root of the right side: 0.236079203 Break this problem into two subproblems by setting (x + -0.3402380953) equal to 0.236079203 and -0.236079203.Subproblem 1
x + -0.3402380953 = 0.236079203 Simplifying x + -0.3402380953 = 0.236079203 Reorder the terms: -0.3402380953 + x = 0.236079203 Solving -0.3402380953 + x = 0.236079203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3402380953' to each side of the equation. -0.3402380953 + 0.3402380953 + x = 0.236079203 + 0.3402380953 Combine like terms: -0.3402380953 + 0.3402380953 = 0.0000000000 0.0000000000 + x = 0.236079203 + 0.3402380953 x = 0.236079203 + 0.3402380953 Combine like terms: 0.236079203 + 0.3402380953 = 0.5763172983 x = 0.5763172983 Simplifying x = 0.5763172983Subproblem 2
x + -0.3402380953 = -0.236079203 Simplifying x + -0.3402380953 = -0.236079203 Reorder the terms: -0.3402380953 + x = -0.236079203 Solving -0.3402380953 + x = -0.236079203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3402380953' to each side of the equation. -0.3402380953 + 0.3402380953 + x = -0.236079203 + 0.3402380953 Combine like terms: -0.3402380953 + 0.3402380953 = 0.0000000000 0.0000000000 + x = -0.236079203 + 0.3402380953 x = -0.236079203 + 0.3402380953 Combine like terms: -0.236079203 + 0.3402380953 = 0.1041588923 x = 0.1041588923 Simplifying x = 0.1041588923Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5763172983, 0.1041588923}
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