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Simplifying -4.905x2 + 19x + -10 = 0 Reorder the terms: -10 + 19x + -4.905x2 = 0 Solving -10 + 19x + -4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. 2.038735984 + -3.873598369x + x2 = 0 Move the constant term to the right: Add '-2.038735984' to each side of the equation. 2.038735984 + -3.873598369x + -2.038735984 + x2 = 0 + -2.038735984 Reorder the terms: 2.038735984 + -2.038735984 + -3.873598369x + x2 = 0 + -2.038735984 Combine like terms: 2.038735984 + -2.038735984 = 0.000000000 0.000000000 + -3.873598369x + x2 = 0 + -2.038735984 -3.873598369x + x2 = 0 + -2.038735984 Combine like terms: 0 + -2.038735984 = -2.038735984 -3.873598369x + x2 = -2.038735984 The x term is -3.873598369x. Take half its coefficient (-1.936799185). Square it (3.751191083) and add it to both sides. Add '3.751191083' to each side of the equation. -3.873598369x + 3.751191083 + x2 = -2.038735984 + 3.751191083 Reorder the terms: 3.751191083 + -3.873598369x + x2 = -2.038735984 + 3.751191083 Combine like terms: -2.038735984 + 3.751191083 = 1.712455099 3.751191083 + -3.873598369x + x2 = 1.712455099 Factor a perfect square on the left side: (x + -1.936799185)(x + -1.936799185) = 1.712455099 Calculate the square root of the right side: 1.308608077 Break this problem into two subproblems by setting (x + -1.936799185) equal to 1.308608077 and -1.308608077.Subproblem 1
x + -1.936799185 = 1.308608077 Simplifying x + -1.936799185 = 1.308608077 Reorder the terms: -1.936799185 + x = 1.308608077 Solving -1.936799185 + x = 1.308608077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.936799185' to each side of the equation. -1.936799185 + 1.936799185 + x = 1.308608077 + 1.936799185 Combine like terms: -1.936799185 + 1.936799185 = 0.000000000 0.000000000 + x = 1.308608077 + 1.936799185 x = 1.308608077 + 1.936799185 Combine like terms: 1.308608077 + 1.936799185 = 3.245407262 x = 3.245407262 Simplifying x = 3.245407262Subproblem 2
x + -1.936799185 = -1.308608077 Simplifying x + -1.936799185 = -1.308608077 Reorder the terms: -1.936799185 + x = -1.308608077 Solving -1.936799185 + x = -1.308608077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.936799185' to each side of the equation. -1.936799185 + 1.936799185 + x = -1.308608077 + 1.936799185 Combine like terms: -1.936799185 + 1.936799185 = 0.000000000 0.000000000 + x = -1.308608077 + 1.936799185 x = -1.308608077 + 1.936799185 Combine like terms: -1.308608077 + 1.936799185 = 0.628191108 x = 0.628191108 Simplifying x = 0.628191108Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.245407262, 0.628191108}
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