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Simplifying 4.2x2 + 7x + -8 = 0 Reorder the terms: -8 + 7x + 4.2x2 = 0 Solving -8 + 7x + 4.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.2 the coefficient of the squared term: Divide each side by '4.2'. -1.904761905 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '1.904761905' to each side of the equation. -1.904761905 + 1.666666667x + 1.904761905 + x2 = 0 + 1.904761905 Reorder the terms: -1.904761905 + 1.904761905 + 1.666666667x + x2 = 0 + 1.904761905 Combine like terms: -1.904761905 + 1.904761905 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 1.904761905 1.666666667x + x2 = 0 + 1.904761905 Combine like terms: 0 + 1.904761905 = 1.904761905 1.666666667x + x2 = 1.904761905 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 1.904761905 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 1.904761905 + 0.6944444447 Combine like terms: 1.904761905 + 0.6944444447 = 2.5992063497 0.6944444447 + 1.666666667x + x2 = 2.5992063497 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 2.5992063497 Calculate the square root of the right side: 1.61220543 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.61220543 and -1.61220543.Subproblem 1
x + 0.8333333335 = 1.61220543 Simplifying x + 0.8333333335 = 1.61220543 Reorder the terms: 0.8333333335 + x = 1.61220543 Solving 0.8333333335 + x = 1.61220543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.61220543 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.61220543 + -0.8333333335 x = 1.61220543 + -0.8333333335 Combine like terms: 1.61220543 + -0.8333333335 = 0.7788720965 x = 0.7788720965 Simplifying x = 0.7788720965Subproblem 2
x + 0.8333333335 = -1.61220543 Simplifying x + 0.8333333335 = -1.61220543 Reorder the terms: 0.8333333335 + x = -1.61220543 Solving 0.8333333335 + x = -1.61220543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.61220543 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.61220543 + -0.8333333335 x = -1.61220543 + -0.8333333335 Combine like terms: -1.61220543 + -0.8333333335 = -2.4455387635 x = -2.4455387635 Simplifying x = -2.4455387635Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7788720965, -2.4455387635}
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