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Simplifying 5x2 + -0.1x + 7.9x + 1 = 0 Reorder the terms: 1 + -0.1x + 7.9x + 5x2 = 0 Combine like terms: -0.1x + 7.9x = 7.8x 1 + 7.8x + 5x2 = 0 Solving 1 + 7.8x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 1.56x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 1.56x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 1.56x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 1.56x + x2 = 0 + -0.2 1.56x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 1.56x + x2 = -0.2 The x term is 1.56x. Take half its coefficient (0.78). Square it (0.6084) and add it to both sides. Add '0.6084' to each side of the equation. 1.56x + 0.6084 + x2 = -0.2 + 0.6084 Reorder the terms: 0.6084 + 1.56x + x2 = -0.2 + 0.6084 Combine like terms: -0.2 + 0.6084 = 0.4084 0.6084 + 1.56x + x2 = 0.4084 Factor a perfect square on the left side: (x + 0.78)(x + 0.78) = 0.4084 Calculate the square root of the right side: 0.639061812 Break this problem into two subproblems by setting (x + 0.78) equal to 0.639061812 and -0.639061812.Subproblem 1
x + 0.78 = 0.639061812 Simplifying x + 0.78 = 0.639061812 Reorder the terms: 0.78 + x = 0.639061812 Solving 0.78 + x = 0.639061812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.78' to each side of the equation. 0.78 + -0.78 + x = 0.639061812 + -0.78 Combine like terms: 0.78 + -0.78 = 0.00 0.00 + x = 0.639061812 + -0.78 x = 0.639061812 + -0.78 Combine like terms: 0.639061812 + -0.78 = -0.140938188 x = -0.140938188 Simplifying x = -0.140938188Subproblem 2
x + 0.78 = -0.639061812 Simplifying x + 0.78 = -0.639061812 Reorder the terms: 0.78 + x = -0.639061812 Solving 0.78 + x = -0.639061812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.78' to each side of the equation. 0.78 + -0.78 + x = -0.639061812 + -0.78 Combine like terms: 0.78 + -0.78 = 0.00 0.00 + x = -0.639061812 + -0.78 x = -0.639061812 + -0.78 Combine like terms: -0.639061812 + -0.78 = -1.419061812 x = -1.419061812 Simplifying x = -1.419061812Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.140938188, -1.419061812}
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