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Simplifying 53.3 = x2 + -0.8x + 0.16 Reorder the terms: 53.3 = 0.16 + -0.8x + x2 Solving 53.3 = 0.16 + -0.8x + x2 Solving for variable 'x'. Combine like terms: 53.3 + -0.16 = 53.14 53.14 + 0.8x + -1x2 = 0.16 + -0.8x + x2 + -0.16 + 0.8x + -1x2 Reorder the terms: 53.14 + 0.8x + -1x2 = 0.16 + -0.16 + -0.8x + 0.8x + x2 + -1x2 Combine like terms: 0.16 + -0.16 = 0.00 53.14 + 0.8x + -1x2 = 0.00 + -0.8x + 0.8x + x2 + -1x2 53.14 + 0.8x + -1x2 = -0.8x + 0.8x + x2 + -1x2 Combine like terms: -0.8x + 0.8x = 0.0 53.14 + 0.8x + -1x2 = 0.0 + x2 + -1x2 53.14 + 0.8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 53.14 + 0.8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -53.14 + -0.8x + x2 = 0 Move the constant term to the right: Add '53.14' to each side of the equation. -53.14 + -0.8x + 53.14 + x2 = 0 + 53.14 Reorder the terms: -53.14 + 53.14 + -0.8x + x2 = 0 + 53.14 Combine like terms: -53.14 + 53.14 = 0.00 0.00 + -0.8x + x2 = 0 + 53.14 -0.8x + x2 = 0 + 53.14 Combine like terms: 0 + 53.14 = 53.14 -0.8x + x2 = 53.14 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = 53.14 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = 53.14 + 0.16 Combine like terms: 53.14 + 0.16 = 53.3 0.16 + -0.8x + x2 = 53.3 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 53.3 Calculate the square root of the right side: 7.300684899 Break this problem into two subproblems by setting (x + -0.4) equal to 7.300684899 and -7.300684899.Subproblem 1
x + -0.4 = 7.300684899 Simplifying x + -0.4 = 7.300684899 Reorder the terms: -0.4 + x = 7.300684899 Solving -0.4 + x = 7.300684899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 7.300684899 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 7.300684899 + 0.4 x = 7.300684899 + 0.4 Combine like terms: 7.300684899 + 0.4 = 7.700684899 x = 7.700684899 Simplifying x = 7.700684899Subproblem 2
x + -0.4 = -7.300684899 Simplifying x + -0.4 = -7.300684899 Reorder the terms: -0.4 + x = -7.300684899 Solving -0.4 + x = -7.300684899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -7.300684899 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -7.300684899 + 0.4 x = -7.300684899 + 0.4 Combine like terms: -7.300684899 + 0.4 = -6.900684899 x = -6.900684899 Simplifying x = -6.900684899Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.700684899, -6.900684899}
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