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Simplifying 0.785x2 + -10x + -1456 = 0 Reorder the terms: -1456 + -10x + 0.785x2 = 0 Solving -1456 + -10x + 0.785x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.785 the coefficient of the squared term: Divide each side by '0.785'. -1854.77707 + -12.7388535x + x2 = 0 Move the constant term to the right: Add '1854.77707' to each side of the equation. -1854.77707 + -12.7388535x + 1854.77707 + x2 = 0 + 1854.77707 Reorder the terms: -1854.77707 + 1854.77707 + -12.7388535x + x2 = 0 + 1854.77707 Combine like terms: -1854.77707 + 1854.77707 = 0.00000 0.00000 + -12.7388535x + x2 = 0 + 1854.77707 -12.7388535x + x2 = 0 + 1854.77707 Combine like terms: 0 + 1854.77707 = 1854.77707 -12.7388535x + x2 = 1854.77707 The x term is -12.7388535x. Take half its coefficient (-6.36942675). Square it (40.56959712) and add it to both sides. Add '40.56959712' to each side of the equation. -12.7388535x + 40.56959712 + x2 = 1854.77707 + 40.56959712 Reorder the terms: 40.56959712 + -12.7388535x + x2 = 1854.77707 + 40.56959712 Combine like terms: 1854.77707 + 40.56959712 = 1895.34666712 40.56959712 + -12.7388535x + x2 = 1895.34666712 Factor a perfect square on the left side: (x + -6.36942675)(x + -6.36942675) = 1895.34666712 Calculate the square root of the right side: 43.535579325 Break this problem into two subproblems by setting (x + -6.36942675) equal to 43.535579325 and -43.535579325.Subproblem 1
x + -6.36942675 = 43.535579325 Simplifying x + -6.36942675 = 43.535579325 Reorder the terms: -6.36942675 + x = 43.535579325 Solving -6.36942675 + x = 43.535579325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.36942675' to each side of the equation. -6.36942675 + 6.36942675 + x = 43.535579325 + 6.36942675 Combine like terms: -6.36942675 + 6.36942675 = 0.00000000 0.00000000 + x = 43.535579325 + 6.36942675 x = 43.535579325 + 6.36942675 Combine like terms: 43.535579325 + 6.36942675 = 49.905006075 x = 49.905006075 Simplifying x = 49.905006075Subproblem 2
x + -6.36942675 = -43.535579325 Simplifying x + -6.36942675 = -43.535579325 Reorder the terms: -6.36942675 + x = -43.535579325 Solving -6.36942675 + x = -43.535579325 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.36942675' to each side of the equation. -6.36942675 + 6.36942675 + x = -43.535579325 + 6.36942675 Combine like terms: -6.36942675 + 6.36942675 = 0.00000000 0.00000000 + x = -43.535579325 + 6.36942675 x = -43.535579325 + 6.36942675 Combine like terms: -43.535579325 + 6.36942675 = -37.166152575 x = -37.166152575 Simplifying x = -37.166152575Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.905006075, -37.166152575}
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